Booklet - 11. Doktorandentreffen Stochastik

Impressum
Paulwin Graewe
Humboldt-Universität zu Berlin
Unter den Linden 6
D-10099 Berlin
Oliver Janke
Humboldt-Universität zu Berlin
Unter den Linden 6
D-10099 Berlin
Moritz Voß
Technische Universität Berlin
Straße des 17. Juni 136
D-10623 Berlin
http://www.dts2015.berlin
Inhaltsverzeichnis
1
Allgemeine Informationen
1.1 Anreise und Unterkunft . . . .
1.2 Veranstaltungsorte . . . . . . .
1.3 Registrierung . . . . . . . . .
1.4 WLAN . . . . . . . . . . . .
1.5 Öffentliche Verkehrsmittel . .
1.6 Verpflegung . . . . . . . . . .
1.7 Grillabend & Konferenzdinner
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4
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2
Danksagung
7
3
Programm
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4
Abstracts
15
5
Teilnehmerliste
42
6
Karten
45
3
1
1.1
Allgemeine Informationen
Anreise und Unterkunft
Die Unterbringung erfolgt in Doppelzimmern im
Airport-Hotel Berlin-Adlershof
Rudower Chaussee 14
12489 Berlin.
Es befindet sich in unmittelbarer Nähe zum Campus Adlershof der
Humboldt-Universität zu Berlin und zum Erwin Schrödinger-Zentrum,
wo die Konferenz am 5. und 7. August stattfinden wird.
Der Check-In am Mittwoch ist ab 15:00 Uhr möglich, der Check-Out muss am
Freitag bis 12:00 Uhr erfolgen. Individuell können mit der Rezeption direkt
vor Ort andere Zeiten vereinbart werden. Das Gepäck kann am Mittwoch und
Freitag im Hotel abgestellt werden.
Anreise zum Airport-Hotel Berlin-Adlershof und zum SchrödingerZentrum:
Berlin Hauptbahnhof/Ostbahnhof: Mit den S-Bahnen S5 (Richtung Strausberg
Nord), S7 (Richtung Ahrensfelde) oder S75 (Richtung Wartenberg) bis Ostkreuz. Dort Umstieg in die S-Bahnen S8 (Richtung Zeuthen), S85 (Richtung
Grünau) oder S9 (Richtung Flughafen Schönefeld) bis Adlershof. Von dort
sind es entlang der Rudower Chaussee fünf Gehminuten bis zum Airport-Hotel
bzw. zehn Gehminuten bis zum Erwin Schrödinger-Zentrum.
Flughafen Tegel: Mit dem Bus TXL (Richtung Alexanderplatz) bis S-Bahnstation Beusselstraße. Von dort mit der S-Bahn S41 (Ring) bis Ostkreuz. Dann
Umstieg in die S-Bahnen S8 (Richtung Zeuthen), S85 (Richtung Grünau) oder
S9 (Richtung Flughafen Schönefeld) bis Adlershof. Von dort sind es entlang
der Rudower Chaussee fünf Gehminuten bis zum Airport-Hotel bzw. zehn
Gehminuten bis zum Erwin Schrödinger-Zentrum.
Flughafen Schönefeld: Mit dem Bus 164 (Richtung S Kaulsdorf) bis Magnusstraße (für Erwin Schrödinger-Zentrum) bzw. bis Walther-Nernst-Straße (für
Aiport-Hotel).
Berlin Südkreuz: Mit den S-Bahnen S45 (Richtung Flughafen Schönefeld)
oder S47 (Richtung Königs Wusterhausen) bis Adlershof. Von dort sind es
entlang der Rudower Chaussee fünf Gehminuten bis zum Airport-Hotel bzw.
zehn Gehminuten bis zum Erwin Schrödinger-Zentrum.
4
1.2
Veranstaltungsorte
Die Tagung findet am 5. und 7. August an der Humboldt-Universität zu
Berlin am
Erwin Schrödinger-Zentrum
Rudower Chaussee 26
12489 Berlin-Adlershof
in den Räumen 0’110 (EG) und 1’304-1’305 (1. OG) statt. Das Tagungsbüro
befindet sich im Raum 1’303 (1. OG).
Am 6. August findet die Tagung an der Technischen Universität Berlin am
Institut für Mathematik
Straße des 17. Juni 136
10623 Berlin-Charlottenburg
in den Hörsaalen MA 041 und MA 042 (EG) statt.
Anfahrt am Donnerstag zum Institut für Mathematik der TU Berlin:
Mit der S-Bahn von Adlershof: Mit den Linien S8 (Richtung Birkenwerder),
S85 (Richtung Waidmannslust) oder S9 (Richtung Pankow) bis Ostkreuz. Dort
Umstieg in die Linien S5 (Richtung Spandau), S7 (Richtung Potsdam) oder
S75 (Richtung Westkreuz), bis zur Station Tiergarten fahren und dann ca.
5 Minuten die Straße des 17. Juni in westliche Richtung hochlaufen (siehe
Karte am Ende der Broschüre). Alternativ kann man auch bis zur Station
Zoologischer Garten fahren und von dort entweder die U-Bahn Linie U2
Richtung Ruhleben nehmen und an der nächsten Station (Ernst-Reuter-Platz)
aussteigen oder mit den Buslinien M45, 245 oder X9 bis Ernst-Reuter-Platz
fahren.
Mit der U-Bahn: Mit der Linie U2 bis zur Station Ernst-Reuter-Platz fahren.
Eine Karte des Campus Charlottenburg der Technischen Universität Berlin
befindet sich am Ende der Broschüre.
1.3
Registrierung
Die Registrierung findet am Mittwoch, den 5. August von 13:00 bis 13:45
Uhr im Erwin Schrödinger-Zentrum im Raum 1’303 statt.
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1.4
WLAN
An beiden Veranstaltungsorten ist eduroam verfügbar.
1.5 Öffentliche Verkehrsmittel
Berlin hat ein gut ausgebautes öffentliches Personennahverkehrssystem. Aktuelle Informationen und Fahrpläne gibt es auf www.bvg.de.
1.6
Verpflegung
Frühstück gibt es für Übernachtungsgäste am Donnerstag und Freitag im
Hotel. Am Mittwochabend findet der Grillabend und am Donnerstagabend
das Konferenzdinner statt (siehe unten).
Während der Kaffeepausen werden Getränke und kleine Snacks angeboten.
Für die Mittagspause am Donnerstag an der TU Berlin gibt es folgende
Möglichkeiten:
• Mathe Café: Direkt im Erdgeschoß des Mathematikgebäudes.
• Personalkantine: Befindet sich im 9. Stockwerk des Mathematikgebäudes. Auch für Studenten und Gäste zugänglich.
• Cafeteria im Architekturgebäude: Auf der Straße des 17. Juni 153, direkt beim Ernst-Reuter-Platz. Wird vom Berliner Studentenwerk betrieben. Barzahlung ist aber möglich!
• Cafeteria “skyline” im TU Hochaus: Am Ernst-Reuter-Platz 7, im
Telekom-Hochaus in der 20. Etage! Schöner Rundblick über die Dächer
von Berlin! Wird ebenfalls vom Berliner Studentenwerk betrieben. Barzahlung ist aber auch hier möglich.
• TU-Mensa: Hardenbergstraße 34, 10623 Berlin. Leider keine Barzahlung möglich, sondern Bezahlung nur mit Mensakarte (also am besten
nur mit einem “Berliner” hingehen)!
1.7
Grillabend & Konferenzdinner
Am Mittwoch gibt es ab 18:30 Uhr einen Grillabend direkt im Restaurant
und Biergarten des Aiport-Hotels Berlin-Adlershof, zu dem alle Teilnehmer
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des Doktorandentreffens eingeladen sind. Neben verschiedenen Fleischsorten wird es auch vegetarische Gerichte und Salate geben. Getränke müssen
individuell bezahlt werden.
Anschließend besteht noch die Möglichkeit, den Abend im studentischen
Begegnungszentrum Motorenprüfstand auf dem Campus-Adlershof (Newtonstr. 16, 12489 Berlin-Adlershof – siehe Karte am Ende der Broschüre)
ausklingen zu lassen.
Das Konferenzdinner findet am Donnerstag auf der MS “Bellevue” statt.
Die Abfahrt ist um 18:15 Uhr von der Schlossbrücke (Charlottenburger
Ufer 1, 10587 Berlin), ca. 2 km vom Mathematik-Gebäude der TU Berlin
entfernt (siehe Karte am Ende der Broschüre für eine Wegbeschreibung).
Während der ca. dreistündigen Tour auf der Spree durch das moderne und
historische Berlin wird es ein reichhaltiges Buffet mit kalten und warmen
Speisen geben. Getränke sind wieder selbst zu zahlen. Die Tour endet gegen
21:30 Uhr an der Friedrichsstraße (Reichstagsufer 18, 10117 Berlin). Von
dort aus kommt man bequem mit den S-Bahnen zurück nach Adlershof oder
kann noch das Berliner Nachtleben erkunden.
2
Danksagung
Wir bedanken uns bei unseren Partnern, ohne deren finanzielle Unterstützung
dieses Doktorandentreffen nicht möglich wäre:
• DMV-Fachgruppe Stochastik e.V.
• Humboldt-Universität zu Berlin, Institut für Mathematik
• Technische Universität Berlin, Institut für Mathematik
• Berlin Mathematical School
• Research Training Group 1845: Stochastic Analysis with Applications
in Biology, Finance and Physics
• International Research Training Group 1792: High Dimensional Non
Stationary Time Series
• DFG-Forschungsgruppe 1735: Structural Inference in Statistics: Adaptation and Efficiency
• Deutsche Gesellschaft für Versicherungs- und Finanzmathematik e.V.
• d-fine GmbH
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3
Programm
Mittwoch, 5. August, HU Berlin (Campus Adlershof)
13:00 – 13:45
13:45 – 14:10
– Registrierung – (Raum 1’303)
– Eröffnung – (Raum 0’110)
Raum 1’304
S TOCHASTIC A NALYSIS AND
TICS (Chair: Paulwin Graewe)
14:15 – 14:35
Claus Griessler
Optimality and cyclical monotonicity
David Prömel
Robust Super-replication for Time-invariant Derivatives
Benedikt Köpfer
Comparison of European Option Prices in Semimartingale Models
14:35 – 14:55
14:55 – 15:15
Raum 1’305
14:15 – 14:35
14:35 – 14:55
14:55 – 15:15
F INANCIAL M ATHEMA -
BAYESIAN S TATISTICS (Chair: Inga Stolz)
Tobias Siems
An EM-Algorithm for the L2-Potts functional
Achim Dörre
Bayesian Estimation of a Proportional Hazards Model
for Doubly Censored Durations
Simone Hermann
Modeling Crack Growth in Fatigue Experiments - A Bayesian Prediction Approach Based on a Nonhomogeneous
Poisson Process
– Kaffeepause –
Raum 1’304
15:45 – 16:05
16:05 – 16:25
16:25 – 16:45
S TOCHASTIC A NALYSIS (Chair: Martin Weidner)
Sara Svaluto-Ferro
Polynomial Preserving Jump-Diffusions on the Unit Interval
Matti Leimbach
Noise-induced strong stability
Jamil Chaker
Eindeutigkeit des Martingal-Problems für eine Klasse von
nichtlokalen Operatoren
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Raum 1’305
15:45 – 16:05
16:05 – 16:25
16:25 – 16:45
M ATHEMATICAL S TATISTICS APPLIED TO R ISK M ANA GEMENT (Chair: Maria Umlauf)
Xiu Xu
Localised Conditional Autoregressive Expectile Model
Philipp Gschoepf
TERES - Tail Event Risk Expectile based Shortfall
Tobias Fissler
Higher order elicitability and Osband’s principle
– Kaffeepause –
Raum 1’304
17:00 – 17:20
17:20 – 17:40
17:40 – 18:00
Raum 1’305
17:00 – 17:20
17:20 – 17:40
17:40 – 18:00
ab 18:30
R ANDOM (D ISCRETE ) S TRUCTURES (Chair: Kathrin
Skubch)
Adrian Gonzalez
An individual-based model for Lenski’s long-term evolution experiment
Julian Gerstenberg
Rémy’s Kette und die Brownsche Exkursion
Felicia Raßmann
Chasing Phase Transitions in Random Discrete Structures
N UMERICAL A NALYSIS OF SDE S (Chair: Stefan Häfner)
Markus Ableidinger
Structure preserving splitting integrators for stochastic
differential equations
Andreas Thalhammer
Mean-square stiffness analysis of stochastic differential
equations
Claudine Leonhard
Approximation of stochastic evolution equations
– Grillabend – (Airport-Hotel Berlin-Adlershof)
9
Donnerstag, 6. August, TU Berlin (Campus Charlottenburg)
Raum MA 041
10:00 – 10:20
10:20 – 10:40
10:40 – 11:00
Raum MA 042
10:00 – 10:20
10:20 – 10:40
10:40 – 11:00
S TOCHASTIC A NALYSIS (Chair: Claus Griessler)
Alexandra Neamtu
Dynamics of Non-densely Defined Stochastic Evolution
Equations
Martin Weidner
Smooth Densities for Rough Differential Equations on
Manifolds
Jens Lueddeckens
Eine inhomogene stochastische Differentialgleichung mit
fraktalem Poisson-Maß und fraktaler Brownscher Bewegung
T IME S ERIES A NALYSIS (Chair: Anna Leister)
Inga Stolz
Komplexität messen: Ein nützliches und interessantes
Werkzeug für die Zeitreihenanalyse – die ordinale Musterverteilung
Maria Umlauf
Analyse zeitdynamischer onkologischer Daten in Abwesenheit eines Ereignisses in der interessierenden Ereigniskategorie
Dennis Dobler
Inference Procedures for Cumulative Incidence Functions
– Kaffeepause –
Raum MA 041
11:15 – 11:35
11:35 – 11:55
Raum MA 042
11:15 – 11:35
11:35 – 11:55
M ARKETS WITH F RICTION (Chair: Moritz Voß)
Mark Feodoria
Portfolio Optimization under fixed Transaction Costs
Thomas Cayé
Local Utility Maximization with Small Nonlinear Price
Impact
N UMERICAL P ROBABILITY (Chair: Claudine Leonhard)
Stefan Häfner
Weak Monte Carlo path generation method with optimal
control variates
Samuel Hetterich
On the chromatic number of random regular graphs
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12:00 – 12:30
Vortrag d-fine GmbH (MA 041)
– Mittagspause –
Raum MA 041
14:00 – 14:20
14:20 – 14:40
14:40 – 15:00
15:00 – 15:20
Raum MA 042
14:00 – 14:20
14:20 – 14:40
14:40 – 15:00
15:00 – 15:20
S TOCHASTIC C ONTROL AND (B)SDE S (Chair: Sara
Svaluto-Ferro)
Maike Klein
An Optimal Stopping Problem with Expectation Constraints
Kai Kümmel
Zur Dynamik von Stochastischen Differentialgleichungen
mit Lévy-Rauschen
Alexandros Saplaouras
Robustness of Backward Stochastic Differential Equations with Jumps
Jasmin Röder
Pfadabhängige BSDEs mit Sprüngen
C ONFIDENCE SETS AND STATISTICAL TESTS (Chair:
Simone Hermann)
Karl Ewald
Confidence Sets Based on the LASSO Estimator
Todor Dinev
Über Buehler-Konfidenzbereiche
Andreas Mändle
An Anderson-Darling approach for testing the goodness
of fit of multivariate data
Daniel Gaigall
Comparison of statistical tests in the paired and independent survey sampling case
– Kaffeepause –
Raum MA 041
15:50 – 16:10
16:10 – 16:30
16:30 – 16:50
P RICE I MPACT IN L IMIT O RDER B OOKS (Chair: Thomas Cayé)
Todor Bilarev
Multiplicative Market Impact Model with Transient Impact: Stability, Absence of Arbitrage and Hedging
Marvin Müller
Stochastic Stefan-type Problems and Limit Order Book
Models
Peter Frentrup
Optimal Liquidation in a Multiplicative Market Impact
Model
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Raum MA 042
15:50 – 16:10
16:10 – 16:30
16:30 – 16:50
ab 18:15
R ANDOM G RAPHS AND R ANDOM WALK IN R ANDOM
E NVIRONMENT (Chair: Felicia Raßmann)
Jan-Erik Lübbers
Gerichtete Irrfahrt auf dem Leitergraph
Felix Hermann
The Partial Duplication Random Graph
Kathrin Skubch
How does the core sit inside the mantle?
– Konferenzdinner auf der “Bellevue” –
(Abfahrt Schlossbrücke, Charlottenburger Ufer 1)
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Freitag, 7. August, HU Berlin (Campus Adlershof)
Raum 1’304
09:30 – 09:50
09:50 – 10:10
10:10 – 10:30
10:30 – 10:50
Raum 1’305
09:30 – 09:50
09:50 – 10:10
10:10 – 10:30
10:30 - 10:50
P ORTFOLIO O PTIMIZATION AND O PTIMAL C ONTROL
(Chair: Mark Feodoria)
Lukas Gonon
Evolution of Firm Size
Hakam Kondakji
Portfoliooptimierung unter partieller Informationen und
Expertenmeinungen in einem Finanzmarkt mit Gaußscher
Drift
Anton Shardin
Optimale Steuerung eines Energiespeichers unter partieller Information
Imke Höfers
Portfolio optimization under dynamic risk contraints
S TATISTICAL E STIMATION (Chair: Andreas Mändle)
Randolf Altmeyer
Covariance estimation in high dimensions using random
matrix theory
Andre Beinrucker
The Wisdom of the Crowds
Anna Leister
Maximum Likelihood Schätzung in hidden Markov Modellen mit zustandsbedingten Mischungen
Gordon Frank
Additives Hazardratenmodell für zufällig doppelttrunkierte Verweildauern
– Kaffeepause –
Raum 1’304
11:20 – 11:40
11:40 – 12:00
12:00 – 12:20
S TOCHASTIC M ODELING IN L IFE S CIENCES (Chair:
Julian Gerstenberg)
Thomas Buder
Field cancerization in the human colon
Markus Doktor
Gibbs Tessellations for Foam Modeling
Laura Bittner
Probabilistic Reliability-Model in Design for Fatigue Life
under Cyclic Thermomechanic Loading
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Raum 1’305
I NTERACTING PARTICLE SYSTEMS AND
TISTICS (Chair: Oliver Janke)
11:20 – 11:40
Alexander Dalinger
On the hydrodynamic behavior of a 1D system with next
neighbor interactions
Peter Czuppon
The one-dimensional cooperative biased voter model
Christoph Kustosz
Depth Based Estimation and Testing for Explosive Autoregressive Processes with Applications
11:40 – 12:00
12:00 – 12:20
12:20 – 12:30
– Verabschiedung – (Raum 0’110)
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ROBUST S TA -
4
Abstracts
Structure preserving splitting integrators for stochastic differential equations
Markus Ableidinger (Johannes Kepler Universität Linz)
In this talk we will discuss stochastic differential equations, where the solution
trajectories are governed by geometric structures as, e.g., energy preservation or dissipation. An efficient strategy for constructing structure preserving
integrators is to split the SDE into subsystems which inherit the geometric
structure and build a numerical integrator by composition of the exact flows of
the subsystems. We apply this approach on SDEs arising in micromagnetism
(stochastic Landau-Lifshitz-Gilbert equation) and neuroscience (stochastic
Jansen and Rit Neural Mass Model).
Covariance estimation in high dimensions using random matrix theory
Randolf Altmeyer (Humboldt-Universität zu Berlin)
Classically, covariance estimation is done using the empirical covariance
which has good properties for large sample size if the dimension is fixed. We
consider the harder problem, when the dimension p and the sample size n
grow as p/n → c for some positive constant c. The key tools are random
matrix theory, as well as some Fourier analysis. We will present the necessary
background and related work. After that, we will extend the known methods
and try to analyze the optimality of the extensions.
The Wisdom of the Crowds
Andre Beinrucker (Universität Potsdam)
In 1907 Sir Francis Galton, a famous British mathematician, took part in a
public event where the weight of an ox was estimated by members of the
audience. He remarked that the median of the estimation was surprisingly
close to the true weight of the ox. This effect was named “Wisdom of the
Crowds” later on and has been applied in many areas of our daily life. In this
talk, we discuss what is needed to make a crowd wise and demonstrate the
concept in practical exercises. Further, I show how the idea is related to the
subject of my dissertation.
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Multiplicative Market Impact Model with Transient Impact: Stability,
Absence of Arbitrage and Hedging
Todor Bilarev (Humboldt-Universität zu Berlin)
In this talk, we will discuss a market model with a single risky asset and a
large trader whose actions can affect its price. Instantaneous (when block
trades are executed) and transient market impact are incorporated in our model.
The price process is given by a positive process (geometric Brownian motion)
multiplied by a non-negative factor depending on the full trading history of the
large trader. We will explain how the wealth process of the large trader evolves
in time by linking our model to the so-called Marcus canonical stochastic
differential equation, for which a Wong-Zakai type of approximation result
holds. Thus, the wealth process for general semimartingale trading strategies
is derived as the limit (in the ucp topology) of wealth processes corresponding
to absolutely continuous strategies. Moreover, we show how the same process
appears as a limit of block-trading approximations. In addition, we show the
absence of arbitrage opportunities (known as NA condition in liquid markets).
In the proposed model we will discuss the optimal trade execution problem
leading to free-boundary singular stochastic optimization problems, and pricing and hedging of European contingent claims, leading to non-linear pricing
PDEs.
Probabilistic Reliability-Model in Design for Fatigue Life under Cyclic
Thermomechanic Loading
Laura Bittner (Bergische Universität Wuppertal)
Blades in gas turbines are exposed to very strong forces caused by a.o. rotation, air pressure and temperature. These forces and temperature loads can be
modeled mathematically by the PDE of thermal elasticity. The stress and strain
states that result from its solution influence the durability of the component.
If this process is repeated cyclically, the formation of cracks due to material
fatigue is unavoidable. Since place and time of appearing cracks at the surface
are not predictable, it is important to integrate a stochastic approach. In particular Poisson-Point-Processes turn out to be appropriate to this task. Furthermore
a Weibull approach is used to determine the failure probability.
These failure probabilities that also depend on the components shape can be
expressed by local cost functionals. Using methods of shape optimization we
proof the existence of optimal designs maximizing the components reliability.
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Field cancerization in the human colon
Thomas Buder (Technische Universität Dresden)
This work is devoted to investigate the formation of a cancer eld within the
human colon by a stochastic approach. In detail, we are interested on the
inuence of the structure of the human colon on the formation of such a cancer
eld. In order to model the human colon, we introduce the two-folded crypt
structure. This structure is composed of complete subgraphs representing
human colonic crypts. Subsequently, basic dynamics of cell proliferation and
cell death on this structure are modeled by utilizing Moran dynamics. The
absorption probabilities and times are calculated and allow a quantitative
estimate of the expected timescale needed to form a cancer field in the human
colon.
Local Utility Maximization with Small Nonlinear Price Impact
Thomas Cayé (Eidgenössische Technische Hochschule Zürich)
We consider a market with one safe asset and one risky asset with general,
not necessarily Markovian dynamics. In this setting, we study the tradeoff
between expected returns, the variance of the corresponding positions, and
nonlinear trading costs proportional to a power of the order flow. In the limit
for small costs, explicit formulas obtain.
This is joint work (in progress) with M. Herdegen and J. Muhle-Karbe.
Eindeutigkeit des Martingal-Problems für eine Klasse von nichtlokalen
Operatoren
Jamil Chaker (Universität Bielefeld)
Sei Zt ein anisotroper stabiler Lévy Prozess mit unterschiedlichen Stabilitätsindizes in jeder Koordinatenrichtung. Im Rahmen dieses Vortrags untersuchen wir stochastische Differentialgleichungen der Form dXt = ξ(Xt− )dZt ,
indem wir das zugehörige Martingal-Problem studieren.
The one-dimensional cooperative biased voter model
Peter Czuppon (Albert-Ludwigs-Universität Freiburg)
Motivated by the phenomenon of cooperation in nature we introduce a model
with nearest-neighbor dynamics. Therefore, we consider a biased voter model
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with types 0 (defectors) and 1 (cooperators). The bias α, the selection parameter, leads to an advantage for the defectors. This interacting particle system is
already well understood and all kinds of limit behavior have been studied. The
analysis relies heavily on the monotonicity of the process.
We expand this model and introduce a cooperation mechanism: individuals
of type 1, the cooperators, help neighboring individuals of either type to reproduce with rate γ to another arbitrary neighboring site. Unfortunately, the
monotonicity of the process is not given anymore under this additional transition such that most of the known methods do not apply in this case.
The goal is to identify the limiting distributions of this interacting particle system and to study the asymptotic behavior of the model for different parameter
ranges and dimensions. In the talk we will only cover the one dimensional
case. Here, we see that coexistence is not possible. For α > γ the defectors
will take over the system, whereas for γ > α the cooperators will survive
almost surely on the infinite lattice.
On the hydrodynamic behavior of a 1D system with next neighbor interactions
Alexander Dalinger (Technische Universität Darmstadt)
We consider a one-dimensional system of particles interacting with each other
over the next neighbors. Starting with an arbitrary configuration of particles,
the aim is to understand the time evolution of the particle density. It can be
proved that the particle density converges in the hydrodynamic limit to a
solution of a nonlinear heat equation. This result will be discussed in the talk.
Über Buehler-Konfidenzbereiche
Todor Dinev (Universität Trier)
Wir stellen eine verallgemeinerte Konstruktionsmethode des kleinsten (bzgl.
Mengeninklusion) monotonen (bzgl. einer “designierten Statistik”) Konfidenzbereiches für einen beliebigen interessierenden Parameter in einem allgemeinen Modell auf einem total prägeordneten Stichprobenraum vor. Diese
Methode, welche von Robert J. Buehler aus dem Jahre 1957 stammt, ist
hauptsächlich in der Zuverlässigkeitstheorie bekannt, kann aber auch im Bereich der Intervallschätzung ganz allgemein angewandt werden und verdient,
unserer Meinung nach, größere Aufmerksamkeit.
Nach der Aufstellung einiger Optimalitätseigenschaften von BuehlerKonfidenzbereichen gehen wir anhand einiger Beispiele kurz auf das Problem
der Wahl einer sinnvollen designierten Statistik ein.
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Inference Procedures for Cumulative Incidence Functions
Dennis Dobler (Universität Ulm)
The analysis of cumulative incidence functions (and more generally of transition probability matrices of non-homogeneous Markov processes) is of great
importance (especially in medical applications) and it constantly gives rise to
new statistical developments. While observations may be incomplete, e.g. due
to random left-truncation and right-censoring, estimation of these probabilities is conducted by employing counting processes and the Aalen-Johansen
estimator. However, results of weak convergence towards a Gaussian process
cannot be utilized straightforwardly since the complicated limiting covariance
structure depends on unknown quantities. Already established tests, which are
popular in the literature, have a simple limit distribution but may have poor
power.
In order to construct asymptotically valid and powerful inference procedures,
we introduce a large variety of resampling techniques using a martingale representation of the Aalen-Johansen estimator. A new aspect to this approach is
given by the possibility to flexibly choose these multipliers dependent on the
data, covering, for instance, the Wild bootstrap as well as the Weird bootstrap.
In doing so, we gain conditional weak convergence towards a Gaussian process
with correct covariance functions resulting in consistent tests and confidence
bands.
For small samples the performance in the competing risks set-up is assessed
via simulation studies illustrating the type I error control and analyzing the
power of the developed tests and confidence bands.
Gibbs Tessellations for Foam Modeling
Markus Doktor (Technische Universität Kaiserslautern)
If we look onto the microstructure of a foam we observe characteristic features
like the length of the edges and the shape of the cells. The common techniques
for modeling use the Laguerre tessellation generated by a parametric point
process (e.g. sphere packing or Poisson process) which are able to deal with the
size of the cell but not with the length of the edges or the shape of the cell. So
we are using a different approach - Gibbs processes - including the geometric
characteristics of the process in the model in contrast to other models. In
the talk we see that an intuitive model causes problems in simulation and
parameter estimation which leads to a generalized model. For this model we
see fast simulation and consistent estimation techniques. Finally we investigate
some examples.
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Bayesian Estimation of a Proportional Hazards Model for Doubly Censored Durations
Achim Dörre (Universität Rostock)
Doubly censored data consist of uncensored, left and right censored data and
occur frequently in survival time contexts. Bayes estimators of a parametric
proportional hazards model for random durations subject to double-censoring
are investigated. In particular, we prove consistency and asymptotic normality
of the Bayes estimators with respect to quadratic loss. In addition, estimators of
standard errors are derived. The proposed model is applied to rating class data
from a large German bank. Initial rating class effect and time effects for rating
transitions are analysed. In the given setting, no conjugate prior distribution is
available. Therefore, the computation of the estimators is performed by use of
MCMC algorithms for which logarithmic ratios of the posterior density are
derived. A simulation study is conducted in order to analyse the finite-sample
performance in comparison to maximum likelihood estimation. It turns out
that parametric Bayes estimators and confidence intervals can be derived in a
consistent manner and are asymptotically normal. Their performance in finite
samples is satisfying and does not require asymptotic justifications. It is argued
that the proposed Bayes estimators are a reasonable alternative to maximum
likelihood estimation for small and moderate sample size.
Confidence Sets Based on the LASSO Estimator
Karl Ewald (Technische Universität Wien)
In a linear regression model with fixed dimension, we investigate the distribution of the LASSO estimator in finite samples as well as in an asymptotic
setup. In finite samples and asymptotically, in the case where the LASSO estimator is tuned to perform conservative model-selection, we derive formulas
for computing the minimal coverage probability of the entire parameter vector
for a large class of sets. This enables the construction of valid confidence sets
based on the LASSO estimator. The choice of shape for the confidence sets is
also discussed. Moreover, in the case where the LASSO estimator is tuned to
enable consistent model-selection, we give a simple confidence set with minimal coverage probability converging to one. The findings are a generalization
of results of Poetscher & Schneider (Electron. J. Stat., 2010).
20
Portfolio Optimization under fixed Transaction Costs
Mark Feodoria (Christian-Albrechts-Universität Kiel)
Mein Thema behandelt die Bestimmung von asymptotisch erwartungsnutzenoptimalen Handelsstrategien bei festen Transaktionskosten. Feste Kosten bedeutet in diesem Zusammenhang, dass jede Transaktion eines Anlegers sein
Vermögen um einen festen Betrag ε reduziert. Betrachtet wird ein Modell aus
einer Anleihe S 0 = 1 und (zunächst) einer Aktie S, deren Preisprozess als
allgemeiner Itō-Prozess
dSt = µt dt + (σt )> dWt
vorausgesetzt wird. Unter diese Klasse von Modellen fällt auch das BlackScholes Modell. Gesucht wird nun ein vorhersehbarer Prozess ϕ, der den
erwarteten Nutzen des Endvermögens maximiert. Dabei beschreibt ϕt die
(zufällige) Anzahl an Aktien im Portfolio zur Zeit t ∈ [0, T ].
Aus einigen heuristischen Überlegungen kann man eine Kandidatenstrategie
ϕ herleiten, die stets in einem Intervall [ϕ∗ + ∆ϕ− , ϕ∗ + ∆ϕ+ ] um die bei
Abwesenheit von Transaktionskosten optimale Strategie ϕ∗ liegt und beim
Erreichen der Grenzen auf ϕ∗ handelt. In meiner Arbeit möchte ich beweisen,
dass der Erwartungsnutzen der obigen Strategie bis auf einen mit den Transaktionskosten ε verschwindenden Term optimal ist.
Kern meines Vortrags sollen die heuristische Herleitung der Kandidatenstrategie und der Beweis zur asymptotischen Optimalität dieser Strategie sein.
Higher order elicitability and Osband’s principle
Tobias Fissler (Universität Bern)
A statistical functional, such as the mean or the median, is called elicitable
if there is a scoring function or loss function such that the correct forecast of
the functional is the unique minimizer of the expected score. Such scoring
functions are called strictly consistent for the functional. The elicitability of a
functional opens the possibility to compare competing forecasts and to rank
them in terms of their realized scores.
In this talk, we explore the notion of elicitability for multi-dimensional functionals and give both necessary and sufficient conditions for strictly consistent
scoring functions. One of the main results is a multi-dimensional version of Osband’s principle. We cover the case of functionals with elicitable components,
but we also show that one-dimensional functionals that are not elicitable can
be a component of a higher order elicitable functional. In the case of the
variance this is a known result. However, an important result of this paper
21
is that spectral risk measures with a spectral measure with finite support are
jointly elicitable if one adds the ‘correct’ quantiles. A direct consequence of
applied interest is that the pair (Value at Risk, Expected Shortfall) is jointly
elicitable under mild conditions that are usually fulfilled in risk management
applications.
This talk is based on a joint work with Johanna F. Ziegel (University of Bern).
The preprint is available at http://arxiv.org/abs/1503.08123.
Additives Hazardratenmodell für zufällig doppelt-trunkierte Verweildauern
Gordon Frank (Universität Rostock)
Dieses Papier beschäftigt sich mit zufälliger Doppeltrunkation, bei welcher die
obere Trunkationsvariable gleich der unteren, plus eine deterministische Variable ist. Über zufällige Punktmaße wird ein Maximum Likelihood Schätzer für
exponentielle Verweildauern und unbekannter Trunkationsverteilung hergeleitet. Zusätzlich wird dieses Exponentialmodell zu einem additiven Hazardratenmodell verallgemeinert. Sowohl Konsistenz als auch asymptotische Normalität
wird bewiesen. Die Zufälligkeit der Anzahl der Beobachtungen, welche bei
zufälliger Trunkation auftritt, wird für beide Modelle berücksichtigt. Eine
Simulationsstudie zeigt, dass dies in eine Verringerung des mittleren quadratischen Fehlers des exponentiellen Modells resultiert. Beide Modelle werden auf
einen Datensatz angewandt, der die Dauern bis zur Insolvenz von Deutschen
Unternehmen beinhaltet.
Optimal Liquidation in a Multiplicative Market Impact Model
Peter Frentrup (Humboldt-Universität zu Berlin)
We describe a market model for trading a single risky asset, in which a large
investor seeks to liquidate his position in an infinite time horizon, while
maximizing expected proceeds. Trading large orders has an adverse effect on
the asset’s price, which is determined by the investor’s current volume impact
and is multiplicative in relation to the current price. The volume impact is a
deterministically mean-reverting process whenever no trade occurs. We justify
why the proceeds should have a certain form, heuristically by describing a
multiplicative limit order book, and also by drawing a link to Marcus type
SDEs. The martingale optimality principle suggests that the two dimensional
state space of volume impact and number of held assets is separated by a
22
free boundary into a wait- and a sell-region. We derive this free boundary
using classical calculus of variations and prove optimality. If time permits,
we discuss a variant of our model with stochastic volume impact, in which
case verification of optimality reduces to showing certain analytic properties
of Hermite functions, some of which remain to be fully proven.
Comparison of statistical tests in the paired and independent survey
sampling case
Daniel Gaigall (Leibniz Universität Hannover)
Let n ∈ N and (X1 , Y1 ), . . . , (X2n , Y2n ) be independent and identically distributed random variables with values in a product set S × S with distribution
L(X1 , Y1 ). In many practical situations one can choose between the experimental design of a paired survey sampling with observations of the independent
and identically distributed random variables (X1 , Y1 ), . . . , (Xn , Yn ) and the
experimental design of an independent survey sampling with observations of
the two independent blocks of independent and identically distributed random
variables X1 , . . . , Xn and Yn+1 , . . . , Y2n .
It is obvious and important to pose the question of the better design. Assume
that the underlying statistical problem is the testing problem of equality of
the marginal distributions, H : L(X1 ) = L(Y1 ), K : L(X1 ) 6= L(Y1 ).
Depending on the kind of experiment, different statistical tests apply.
In this talk, the comparison of such tests will be done by using asymptotic
relative efficiencies of statistical tests. Of course, this efficiencies depend on
the distribution L(X1 , Y1 ). The focus is on the practical most important case
of multivariate normal distribution.
Rémy’s Kette und die Brownsche Exkursion
Julian Gerstenberg (Leibniz Universität Hannover)
Ein klassisches Resultat (D. Aldous, u.a.) über die Asymptotik zufälliger
ebener Bäume besagt: Ist Tn ein gleichverteilter zufälliger binärer Baum mit
n Blättern und HT0 n der zugehörige geeignet standardisierte Harris-Pfad (oder
auch “Dyckpfad“) zu Tn , so konvergiert HT0 n mit n → ∞ in Verteilung gegen
eine Brownsche Exkursion B ex (der Länge 1).
Im Vortrag wird nun zunächst Rémy’s Kette vorgestellt, eine Markovkette
T = (Tn )n≥1 , bei der Tn für alle n ein gleichverteilter binärer Baum mit
n Blättern ist. Das bekannte Resultat über Verteilungskonvergenz wird in
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dieser Situation verschärft; aus der Verteilungskonvergenz wird eine fastsicher gleichmäßige Konvergenz gegen eine Brownsche Exkursion B ex , in
Zeichen:
HT0 n −→glm. B ex fast sicher für n → ∞.
Dieser Limes stellt sich als “bestmöglicher“ Limes zu Rémy’s Kette dar: B ex
erzeugt die terminale σ-Algebra von T (modulo P ), in Zeichen:
\
σ(Tn , Tn+1 , . . . ).
σ(B ex ) =P T (T ) :=
n≥1
Insbesondere besitzt jede Zufallsgröße X, die fast-sicherer Limes einer Folge
von Zufallsgrößen der Gestalt f (Tn ) ist, eine Darstellung als X = Φ(B ex )
(fast sicher) für eine passende Funktion Φ.
Im Vortrag wird (grob) skizziert, wie man dieses Resultat ausgehend von der
bekannten Verteilungsasymptotik erhalten kann. Wichtige Hilfsmittel dabei
sind Martingalkonvergenzsätze und der Satz von Hewitt-Savage.
Der Beweis liefert als einfaches Korollar eine fundamentale Eigenschaft der
Brownschen Exkursion: Mit kB ex k := sup0≤t≤1 B ex (t) gilt
ex B
ex
,
σ (B ) =P σ
kB ex k
in Worten: Skaliert man eine Brownsche Exkursion auf Maximalhöhe 1, so
geht keine Information verloren. Insbesondere kann man kB ex k aus der normierten Exkursion zurückgewinnen (fast sicher).
Evolution of Firm Size
Lukas Gonon (Eidgenössische Technische Hochschule Zürich)
Recently, mathematical theories for optimal investment have been proposed
that aim to base portfolio selection on quantities that are easy to observe,
such as market capitalizations, rather than on quantities which can only be
estimated with substantial error, such as growth rates and volatilities. What
we propose in this talk is a very simple mechanism to explain why the relative
size of a firm in the market could be informative about its performance: We
suppose that firms are created at random times, each of them getting assigned
a randomly chosen individual growth rate and volatility. The size of each firm
then evolves as a geometric Brownian motion with this drift and volatility until
it disappears from the market after a random lifetime. At any fixed time, there
is a finite number of firms alive and their sizes contain information about their
24
drifts and volatilities. Under suitable distributional assumptions, we are able
to find the conditional distribution of the growth rate and the volatility given
the current size of a firm, and this can then be used to make portfolio choices
based on the observed sizes.
This is a joint work with Chris Rogers.
An individual-based model for Lenski’s long-term evolution experiment
Adrian Gonzalez (Technische Universität Berlin)
The Lenski experiment investigates the long-term evolution of bacterial populations. Its design allows the direct comparison of the reproductive fitness of an
evolved strain with its founder ancestor. It was observed by Wiser et al. (2013)
that the relative fitness over time increases sublinearly, a behaviour which is
commonly attributed to effects like clonal interference or epistasis. In this
talk, we present an individual-based probabilistic model that captures essential
features of the design of the Lenski experiment. We assume that each beneficial
mutation increases the individual reproduction rate by a fixed amount, which
corresponds to the absence of epistasis in the continuous-time (intraday) part
of the model, but leads to an epistatic effect in the discrete-time (interday)
part of the model. Using an approximation by near-critical Galton-Watson
processes, we prove that under some assumptions on the model parameters
which exclude clonal interference, the relative fitness process converges, after
suitable rescaling, in the large population limit to a power law function.
The talk is based on a joint work with Noemi Kurt, Anton Wakolbinger and
Linglong Yuan.
Optimality and cyclical monotonicity
Claus Griessler (Universität Wien)
The concept of cyclical monotonicity is crucial in optimal transport. Under
mild assumptions on a cost function c, defined on the product of two Polish
spaces X and Y , a probability measure γ is known to be a cost-minimizing
coupling of probabilities µ on X and ν on Y , if and only if γ is concentrated on
a cyclically monotone set. Beiglböck and Juillet (2014) modified the concept
for martingale transport and re-established the equivalence result using more
restrictive assumptions on the cost function. In this talk, I shall present further
variations of these connections. The necessity part can be generalized to a
very large class of problems, including optimal transport with a prescribed
25
continuum of marginal measures. Regarding sufficiency, the situation is more
complicated, but it can be shown that the restrictions on the cost function
in martingale transport can be considerably relaxed. Furthermore, cyclical
monotonicity turns out to be sufficient in optimal transport with n given
marginals if the cost function satisfies a mild integrability condition.
Based on joint work with Mathias Beiglböck and Augusto Gerolin, respectively.
TERES - Tail Event Risk Expectile based Shortfall
Philipp Gschoepf (Humboldt-Universität zu Berlin)
A flexible framework for the analysis of tail events is proposed. The framework contains tail moment measures that allow for Expected Shortfall (ES)
estimation. Connecting the implied tail thickness of a family of distributions
with the quantile and expectile estimation, a platform for risk assessment is
provided. ES and implications for tail events under different distributional
scenarios are investigated, particularly we discuss the implications of increased
tail risk for mixture distributions. Empirical results from the US, German and
UK stock markets, as well as for the selected currencies indicate that ES can
be successfully estimated on a daily basis using a one-year time horizon across
different risk levels.
Weak Monte Carlo path generation method with optimal control variates
Stefan Häfner (Universität Duisburg-Essen)
In this talk, a novel modification of the Single level Monte Carlo path simulation approach, allowing for further significant complexity reduction, is
introduced. The idea of the modification is using the method of control variates
to remove the variance. Under a proper choice of control variates, one can reduce the complexity order below ε−2 with ε being the precision to be achieved.
These theoretical results are illustrated by several numerical examples.
The Partial Duplication Random Graph
Felix Hermann (Albert-Ludwigs-Universität Freiburg)
We study a model for an evolving random graph: At each time step a vertex v
is chosen u.a.r. and partially duplicated. That means a new node w is added to
26
the network after which each neighbor of v is connected to w with probability
p independently. Here, p ∈ (0, 1) denotes the only parameter of our model. In
comparison to the extensively discussed preferential attachment models, this
process has substantially different topological properties, while its asymptotics
are not yet well understood. Following a brief introduction, this talk will
outline one issue in particular, i.e. the vast appearance of vertices without any
edges, and its connection to the often desired power-law property. The main
tool we used to compute the limit of the degree distribution is a duality to
a piecewise deterministic Markov process. In conclusion to the presentation
further results and open questions will be discussed.
Modeling Crack Growth in Fatigue Experiments - A Bayesian Prediction
Approach Based on a Nonhomogeneous Poisson Process
Simone Hermann (Technische Universität Dortmund)
In constructional engineering, experiments of material fatigue are very expensive and therefore seldom. In our research project on “Statistical methods for
damage processes under cyclic load” of the collaborative research centre 823
from the TU Dortmund University, the engineers conducted an experiment, in
which they set several prestressed concrete beams under cyclic load, starting
with initial cracks. The observed crack widths exhibit irregular jumps with
increasing frequency which influence the growth process substantially. Sound
measurements provide information concerning the break times of the tension
wires which perfectly match the observed jumps in the crack width data. This
finding has important implications for the project aiming to find a stochastic
model that describes – and ultimately allows to predict – the development of
the crack width curve.
A nonhomogeneous Poisson process is defined to describe the number of
broken tension wires over time. For the crack width curve, expert knowledge
from the engineering researchers is used to form a stochastic model dependent
on the counting process. A Bayesian estimation procedure and the resulting
predictive distribution will be presented, once for the Poisson process and
further in turn for the whole crack width process conditional on the Poisson
process.
On the chromatic number of random regular graphs
Samuel Hetterich (Goethe-Universität Frankfurt a.M.)
Determining the chromatic number of random graphs is one of the longeststanding challenges in probabilistic combinatorics. For the Erdős-Rényi model,
27
the single most intensely studied model in the random graphs literature, the
question dates back to the seminal 1960 paper that started the theory of random
graphs.
Apart from Erdős-Rényi, the model that has received the most attention certainly is the random regular graph G(n, d). We provide an almost complete
solution to the chromatic number problem on G(n, d), at least in the case that
d remains fixed as n → ∞. Our main result is:
There is a sequence (εk )k≥3 with limk→∞ εk = 0 such that the following is
true.
1. If d ≤ (2k − 1) ln k − 2 ln 2 − εk , then G(n, d) is k-colorable w.h.p.
2. If d ≥ (2k − 1) ln k − 1 + εk , then G(n, d) fails to be k-colorable w.h.p.
This implies that for every integer k exceeding a certain constant k0 we identify
a number dk−col such that G(n, d) is k-colorable w.h.p. if d < dk−col and
non-k-colorable w.h.p. if d > dk−col .
In my talk I will give a overview about the technical improvments intuition
driven by non-rigorous statistical mechanics work on random graph coloring
leading to the result.
This is joint work with Amin Coja-Oghlan and Charilaos Efthymiou.
Portfolio optimization under dynamic risk contraints
Imke Höfers (BTU Cottbus-Senftenberg)
We consider an investor faced with the classical portfolio problem of optimal
investment in a log-Brownian share and a fixed-interest bond, but constrained
to choose portfolio and consumption strategies which reduce the corresponding shortfall risk. Risk measures are calculated for short time intervals and
imposed on the strategy as a risk constraint. To derive optimal strategies under
this constraint, we apply dynamic programming techniques and combine the
resulting Hamilton-Jacobi-Bellman equation with the method of Lagrange
multipliers to handle the constraint. An approximate solution to the constrained
portfolio problem is obtained by using a policy improvement algorithm. In
addition we present various numerical methods to solve the partial differential
equations arising in this algorithm. Our numerical results indicate that the
effect of the risk constraint is very small, that is the investor is not losing very
much compared to the unconstrained case.
28
An Optimal Stopping Problem with Expectation Constraints
Maike Klein (Friedrich-Schiller-Universität Jena)
We maximize the expected reward E[f (Xτ )] for a time-homogeneous diffusion X over stopping times τ with E[τ ] ≤ T . The associated value function is
compared to the one obtained in the classical problem where stopping times
with values in [0, T ] are considered. Our optimal stopping problem is reformulated as an optimal control problem with controlled time horizon and it is
shown that under certain assumptions the value function is the unique solution
of a variational inequality.
Portfoliooptimierung unter partieller Informationen und Expertenmeinungen in einem Finanzmarkt mit Gaußscher Drift
Hakam Kondakji (BTU Cottbus-Senftenberg)
In diesem Vortrag untersuchen wir optimale Portfoliostrategien für nutzenmaximierende Investoren in einem zeitstetigen Finanzmarktmodell mit partieller
Information über die Drift. Die Drift bzw. mittlere Aktienrendite wird durch
einen Ornstein-Uhlenbeck-Prozess modelliert, welcher nicht direkt beobachtbar ist. In klassischen Modellen nimmt man an, dass Informationen über die
Drift lediglich aus Beobachtungen der Aktienpreise gewonnen werden können.
Die daraus gewonnen Schätzungen besitzen oft nur eine unbefriedigende
Genauigkeit, da Drifteffekte in den Aktienpreisen typischerweise von einer
hohen Volatilität überlagert werden. Aus diesem Grunde versuchen Praktiker zusätzliche Informationsquellen wie z.B. Unternehmensberichte, Ratings,
Nachrichtenmeldungen, Empfehlungen von Analysten oder ihre eigene subjektiven Einschätzungen über die zukünftige Renditen in die Schätzungen
mit einzubeziehen. Diese als Expertenmeinungen bezeichneten Informationen
werden mit den Aktienpreisbeobachtungen kombiniert, um eine verbesserte
Driftschätzung zu erhalten. Im Falle von erwartungstreuen Expertenmeinungen verbessert dies die Varianz des Schätzers und führt zu einer besseren
Performance der darauf aufbauenden optimalen Portfoliostrategien.
Dieser Ansatz kann als eine zeitstetige Version des aus der Literatur bekannten
statischen Black-Litterman-Modells betrachtet werden. Auch mit Expertenmeinungen bleibt die Drift nur partiell beobachtbar. Die beste Schätzung für
die Drift ist die bedingte Erwartung gegeben die verfügbaren Informationen,
der sogenannte Filter. Werden in dem betrachteten Modell mit Gaußscher Drift
lediglich Aktienpreise beobachtet, führt dies zum klassichen Kalman-Filter.
In dieser Arbeit betrachten wir nun zusätzlich Expertenmeinungen, die zu
zufälligen Zeitpunkten eintreffen und als Gaußsche Zufallsgrößen modelliert
29
werden. Hierfür konstruieren wir mittels eines markierten Punktprozesses den
entsprechenden modifzierten Filter.
Für das dynamische Portfoliooptimierungsproblem mit einer Nutzenfunktion
geben wir in speziellen Fällen explizite Lösungen für die Wertfunktion des
Problems an. Wir präsentieren numerische Ergebnisse und diskutieren den
Wert der zusätzlichen Informationen.
Comparison of European Option Prices in Semimartingale Models
Benedikt Köpfer (Albert-Ludwigs-Universität Freiburg)
A set of real-valued functions F induces a so-called integral stochastic order
on the set of random variables by
X ≤F Y ⇔ E[f (X)] ≤ E[f (Y )], ∀f ∈ F.
In terms of financial mathematics the right-hand side can be interpreted as
prices of European options with payoff function f . Assume there are two different models (Xt )t≥0 , (Yt )t≥0 describing the evolution of asset prices under
the same pricing measure. Then a stochastic order at maturity XT ≤F YT
directly provides an ordering of the corresponding European option prices.
Conditions for such comparison results can be obtained with methods from
stochastic analysis and semigroup theory. Results of this type are known for
Markov processes and if one process is markovian and the other a semimartingale. We will discuss approaches to compare two semimartingales.
Zur Dynamik von Stochastischen Differentialgleichungen mit Lévy–
Rauschen
Kai Kümmel (Friedrich-Schiller-Universität Jena)
Für eine spezielle Klasse stochastischer Differentialgleichungen (MSDEs)
wird eine Verallgemeinerung des Satzes von Hartman–Grobman vorgestellt.
Speziell wird gezeigt, dass bestimmte MSDEs und deren Linearisierung lokal
konjugiert sind. Ferner werden grundlegende dynamische Eigenschaften für
analoge Gleichungen mit Gedächtnis (SDDEs) gezeigt.
30
Depth Based Estimation and Testing for Explosive Autoregressive Processes with Applications
Christoph Kustosz (Technische Universität Dortmund)
We introduce methods to analyse growth models based on autoregressive equations with errors which do not satisfy standard assumptions. In particular error
distributions just satisfying med(En ) = 0 are considered under the additional
assumption that the underlying process is a growth process.
We propose statistics based on simplicial depth and derive asymptotic distributions for this statistics to construct asymptotic tests. Further parameter
confidence sets and depth based estimators are defined. Thereby, for example,
simultaneous parameter confidence sets for nonlinear autoregressive models
can be found. The resulting methods are then compared with common estimators, tests, and confidence sets to illustrate their robustness with respect to
deviations from normally distributed errors.
Based on the Paris-Erdogan equation the methods can be applied to crack
growth in pre-stressed concrete, where the experimental conditions imply
skewed errors and growth processes quite naturally. In addition we discuss an
example in finance to show other potential fields of application.
Noise-induced strong stability
Matti Leimbach (Technische Universität Berlin)
It is a well known fact that additive noise can turn an explosive ODE into a
non-explosive SDE. In many cases, one can even show the existence of an
unique invariant probability measure of the corresponding Markov process.
This phenomenon is often called noise-induced stabilization or noise-induced
stability. We investigate whether the noise can induce a stronger concept of
stability - the existence of a random attractor. We call such a phenomenon
noise-induced strong stability. First, we present an example which shows that
these two concept are not the same. Second, we show that noise-induced strong
stability can indeed occur.
Maximum Likelihood Schätzung in hidden Markov Modellen mit zustandsbedingten Mischungen
Anna Leister (Philipps-Universität Marburg)
Basierend auf neuen Resultaten bezüglich der Identifizierbarkeit von nichtparametrischen hidden Markov Modellen untersuchen wir Maximum Likelihood
31
Schätzung in hidden Markov Modellen mit zustandsbedingten allgemeinen
Mischungen. Wir beweisen, dass ein Maximum Likelihood Schätzer existiert
und die zugehörigen Mischungsverteilungen endlichen Träger besitzen. Weiterhin diskutieren wir die Konsistenz des Schätzers und zeigen insbesondere,
dass die zustandsbedingten Mischungsdichten konsistent geschätzt werden
können, auch ohne die Identifizierbarkeit des Mischungsmodells vorauszusetzen. Numerische Eigenschaften und Vergleiche zur parametrischen Schätzung
werden anhand von Simulationen untersucht.
Approximation of stochastic evolution equations
Claudine Leonhard (Universität zu Lübeck)
Various phenomena in e.g. biology or geology can be modeled with stochastic
evolution equations. We are concerned about finding a solution to this type of
equation. We give a short introduction to stochastic evolution equations; a notion of a solution for parabolic semilinear equations is presented and the random
process driving it, the Q-Wiener process, is defined. Analytical solutions to
stochastic evolution equations are usually not computable, therefore numerical
approximation schemes are in need. The solution process belongs to a Hilbert
space of infinite dimension, so the approximation requires a discretization in
time and space and an approximation of the Q-Wiener process. We illustrate
the specialities inherent in devising numerical schemes for these equations.
Gerichtete Irrfahrt auf dem Leitergraph
Jan-Erik Lübbers (Technische Universität Darmstadt)
Wir betrachten eine gerichtete Irrfahrt auf einem Graphen, der durch Perkolation aus dem Leitergraphen Z × {0, 1}, bedingt auf die Existenz eines
unendlichen Pfades, entsteht. Die betrachtete Irrfahrt soll dazu neigen, sich
“nach rechts” zu bewegen. Es zeigt sich, dass sie transient ist und ein kritischer
Wert existiert, sodass die Irrfahrt sich genau dann mit positiver Geschwindigkeit fortbewegt, wenn ihr bias unterhalb dieses Wertes liegt. In dieser Situation
stellt sich die Frage, ob die Irrfahrt einem zentralen Grenzwertsatz genügt.
32
Eine inhomogene stochastische Differentialgleichung mit fraktalem
Poisson-Maß und fraktaler Brownscher Bewegung
Jens Lueddeckens (Martin-Luther-Universität Halle-Wittenberg)
Ziel des Vortrags ist es, die Existenz und Eindeutigkeit einer Lösung einer
inhomogenen stochastischen Differentialgleichung mit fraktaler Brownscher
Bewegung und fraktalem Poisson-Maß im Hida-Raum (S)−1 nachzuweisen.
Hierfür werden zunächst der Hida-Raum (S)−1 , die fraktale Brownsche
Bewegung sowie das fraktale Poisson-Maß eingeführt und die HermiteTransformation für Elemente des (S)−1 vorgestellt. Im Anschluss wird ein
Existenz- und Eindeutigkeitssatz bezüglich der Lösbarkeit einer inhomogenen
fraktalen stochastischen Differentialgeichung formuliert.
Abschließend werden noch Zusammenhänge zwischen dem L2 (Ω) und dem
(S)−1 sowie Anwendungsmöglichkeiten des Existenz- und Eindeutigkeitssatzes im Raum L2 (Ω) aufgezeigt.
An Anderson-Darling approach for testing the goodness of fit of multivariate data
Andreas Mändle (Carl von Ossietzky Universität Oldenburg)
In the fields of finance and insurance we often face the problem of modelling
extremal events, e.g. when measuring the risk of holding an equity portfolio
or the insurance risk of possible losses in different lines of business. This
involves making distributional assumptions for multivariate, sometimes even
high-dimensional data. It has been frequently observed that in practice tails
are heavier than “normal” and extremes appear in clusters, indicating tail dependence. In such cases the assumptions of normality are violated. Therefore
there is often uncertainty if the normal assumption can still be justified.
In the univariate case a popular method of testing the assumption of normality
is by using the Anderson-Darling test. It is known for its strong power, especially when detecting deviations in the tails of a distribution. Here a possible
generalization of the Anderson-Darling test to the multivariate case will be
considered. Although some theoretical results about a multivariate extension
of the multivariate Anderson-Darling statistic are already known, so far its
application in a multivariate test seemed inconvenient, as the calculation of the
n-variate test statistic required the calculation of an n-dimensional integral.
Here, a calculation formula of this multivariate Anderson-Darling statistic
for finite, multidimensional samples will be presented. Using this formula
immensely simplifies the calculation and thus serves as one key ingredient
to facilitate the practical use of the test. In a multivariate example setting it
33
will be demonstrated how the test can be applied, to test the assumption of
a multivariate normal distribution. Although it will be referred to methods
that allow simulating the asymptotic statistic, conveniently and preferably
the sample quantiles will be computed using Monte-Carlo simulations. In
order to evaluate the use of this new approach in comparison with the other
tests, the test which is proposed here will run against the widely used tests for
multivariate normality.
Stochastic Stefan-type Problems and Limit Order Book Models
Marvin Müller (Technische Universität Dresden)
We introduce a class of price-time-continuous models for the limit order book
density, where the evolution of buy and sell side is described by a semilinear
second-order SPDE and the mid price process defines a moving boundary
separating buy and sell side. Following empirical observations by Cont et al.
(2013) and Lipton et al. (2013) we assume price changes to be determined by
the bid-ask imbalance. The resulting limit order book model can be considered
as a generalization of the linear stochastic Stefan problem introduced by Kim,
Sowers and Zheng (2012).
In order to show existence of a solution we transform the problem into a
stochastic evolution equation, where the boundary interaction leads to an
additional drift. Regularity properties of the linear part in the equation allow
to control the non-linearities and establish (local) existence and uniqueness
results. This provides a framework for further analysis of the problem.
Dynamics of Non-densely Defined Stochastic Evolution Equations
Alexandra Neamtu (Friedrich-Schiller-Universität Jena)
We consider a class of stochastic evolution equations with a non-densely
defined linear part. Such situations can occur due to additional restrictions that
are incorporated in the domain of a linear operator. Our theory is motivated
by the deterministic case considered by P. Magal and S. Ruan (2010). We
can transform such a SDE into a pathwise problem, from which we derive
a random dynamical system. Furthermore, we investigate the existence of
random fixed points and attractors. As applications, we analyze population
models, transport equations with nonlinear boundary conditions and parabolic
equations with nonlocal boundary conditions under stochastic influences.
34
Robust Super-replication for Time-invariant Derivatives
David Prömel (Humboldt-Universität zu Berlin)
The connection between model-independent pricing and the Skorokhod embedding problem has been a driving force in robust finance for the last decade.
We establish a general pricing-hedging duality for financial derivatives which
are susceptible to the Skorokhod approach. Using Vovks approach to mathematical finance we derive a model-independent super-replication theorem in
continuous time, given information on finitely many marginals. Our result covers a broad range of exotic derivatives, including lookback options, discretely
monitored Asian options, and options on realized variance.
The talk is based on a joint work with M. Beigleböck, A. M. G. Cox, M.
Huesmann and N. Perkowski.
Chasing Phase Transitions in Random Discrete Structures
Felicia Raßmann (Goethe Universität Frankfurt a.M.)
The study of random discrete structures has been an active field of research since the pioneering work of Erdős and Rényi on random graphs in the 1950s/60s
and has since then played a key role in combinatorics. In particular the identification of phase transitions, where a small change of a parameter entails a
huge change in the structure of the outcome of the experiment, has been of
great interest. One popular example for a phase transition is the emergence
of a giant component in random graphs. Over the past decade, progress has
been made in studying phase transitions in what physicists call “disordered
systems“. These systems exhibit a structure where the geometry of interactions
is determined by a sparse random graph or hypergraph. The mathematical
rigorous study of disordered systems is very demanding, but physicists have
developed analytic, non-rigorous methods to put forward precise conjectures
on the location and nature of phase transitions in these systems. The challenge
is now to prove the predictions.
In this talk we investigate random hypergraph 2-coloring, the problem of coloring a random hypergraph H(n, p) containing n vertices and each hyperedge
with probability p independently with two colors such that no monochromatic
edge exists. We present the predictions for phase transitions in this model and
what we can actually prove at the moment. We provide an insight into the
methods we use, such as the second moment method and the so called “planted
model“.
35
Pfadabhängige BSDEs mit Sprüngen
Jasmin Röder (Justus-Liebig-Universität Gießen)
Wir untersuchen pfadabhängige BSDEs mit Sprüngen, wobei die Pfadabhängigkeit in diesem Zusammenhang die Abhängigkeit des Generators
und der BSDE-Endbedingung von einem Pfad eines adaptierten càdlàg Prozesses X meint. Für jeden zur Zeit t ∈ [0, T ] gestoppten Pfad γt ist die zu
untersuchende BSDE von der Form
Z T
Yγt (s) = Φ(Xγt ,T ) +
f (r, Xγt ,r , Yγt (r−), Zγt (r), Uγt (r))dr
s
Z
−
T
Z
T
Z
Zγt (r)dW (r) −
s
Uγt (r, x)Ñ (dr, dx)
s
Rl
für s ∈ [t, T ]. Der zum Zeitpunkt T gestoppte Pfad Xγt ,T ist definiert durch
Xγt ,T (u) = γ(u)1[0,t) (u) + (γ(t) + X(u) − X(t))1[t,T ] (u)
für u ∈ [0, T ]. Wir untersuchen die Existenz und die Eindeutigkeit der Lösung
einer solchen BSDE und beweisen außerdem den zugehörigen Vergleichssatz.
Des Weiteren analysieren wir die Pfaddifferenzierbarkeit der Lösung dieser
BSDE und zeigen, dass diese Pfadableitungen wieder eine eindeutige Lösung
einer pfadabhängigen BSDE mit Sprüngen ist. Ein weiteres Resultat ist die
Verbindung einer pfadabhängigen PIDE und der Lösung einer pfadabhängigen
BSDE mit Sprüngen.
Robustness of Backward Stochastic Differential Equations with Jumps
Alexandros Saplaouras (Technische Universität Berlin)
The last 25 years due to the seminal paper of Pardoux and Peng, Backward
Stochastic Differential Equations have gained a lot of attention due to their
applications in stochastic control, theoretical economics, stochastic differential
games and financial mathematics. In the first part of the current work we
present a general result of existence and uniqueness of solutions of BSDEJs
driven by a square integrable martingale. We will proceed by presenting the
robustness of the solutions, i.e. the continuity of the operator which maps the
standard data (in a general sense) to the solution of the BSDEJ. An immediate
application of the robustness property is the Euler scheme, i.e. the solution of
the discretization of a BSDEJ driven by a square integrable Feller martingale
with independent increments converges to the solution of the initial BSDEJ.
36
Optimale Steuerung eines Energiespeichers unter partieller Information
Anton Shardin (BTU Cottbus-Senftenberg)
Die zunehmende Einspeisung von Strom aus zeitlich und räumlich fluktuierenden und schwer prognostizierbaren erneuerbaren Energiequellen wie Sonne
und Wind führt zu neuartigen Problemen beim Ausgleich von Angebot und
Nachfrage auf dem Strommarkt und in den Übertragungsnetzen. In diesem
Zusammenhang gewinnen Energiespeicher wie z.B. Pumpspeicherkraftwerke
an Bedeutung. Deren Aufgabe ist es, Strom in Zeiten großen Angebotes aufzunehmen und bei hoher Nachfrage wieder zurück in das Stromnetz einzuspeisen.
Neben zahlreichen technischen Fragen zur Entwicklung von leistungsfähigen
und kostengünstigen Speichern entsteht auch das Problem der ökonomischen
Bewertung derartiger Speicher auf dem Energiemarkt.
Eine solche Bewertung erfordert eine angemessene Modellierung der fluktuierenden Stromeinspeisung aus erneuerbaren Energieträgern durch stochastische
Prozesse. Grundidee der Speicherbewertung ist, den erwarteten Zahlungsstrom,
welcher die Kosten für den Kauf von Energie (Laden) und die Gewinne aus
dem Verkauf von Energie (Entladen) enthält, durch eine geeignet gewählte
Speicherstrategie zu maximieren. Der bei der Lösung dieses Optimierungsproblemes entstehende optimale Zielfunktionswert kann zugleich als der faire
Preis einer Realoption interpretiert werden. Mit der optimalen Speicherstrategie kann der Speichermanager entscheiden, zu welchem Zeitpunkt welche
Menge an Energie zu laden bzw. zu entladen ist.
Den Energiepreis beschreiben wir durch einen Ornstein-Uhlenbeck Prozess,
dessen Mean-Reversion Level von einem nicht direkt beobachtbaren Faktorprozess abhängt. Dieser Faktorprozess beschreibt den Zustand des Energiemarktes
und wird als Markovkette angesetzt. Das resultierende Optimalsteuerungsproblem unter partieller Information kann durch Aufnahme des Filters für den
Faktorprozess in ein Problem unter vollständiger Information transformiert
werden. Für dessen Lösung untersuchen wir die zugehörige Hamilton-JacobiBellman-Gleichung. Die Lösung dieser partiellen Differentialgleichung gelingt nur numerisch unter Verwendung von Differenzenverfahren und eines
Semi-Lagrangeschen Approximationsschemas. Wir präsentieren numerische
Ergebnisse für ein Steuerungsproblem mit endlichem Zeithorizont.
An EM-Algorithm for the L2-Potts functional
Tobias Siems (Universität Greifswald)
We assume a dataset with normal distributed data, which is subject to successive changes in mean. The goal is to predict the time points where the changes
37
happen. This can be achieved by minimizing the so called Potts functional. The
problem is that the Potts functional and therefore the estimated changepoints
depend on at least one crucial parameter. In my talk I will give a brief overview
about the Potts functional and how it can be translated into a stochastic model,
by using “spike and slab” priors. At this end I will show the EM algorithm for
the estimation of the parameters of the Potts functional.
How does the core sit inside the mantle?
Kathrin Skubch (Goethe Universität Frankfurt a.M.)
For any k ≥ 3 the k-core Ck (G) of a graph G is defined as the (unique)
maximal subgraph of G of minimum degree k. For fixed d > 0 let G(n, d/n)
denote the random graph on the vertex set [n] = {1, . . . , n} in which any
two vertices are connected with probability p = d/n independently. Pittel,
Wormald and Spencer were the first to determine the precise threshold dk
beyond which the k-core Ck (G(n, d/n)) is non-empty w.h.p. [Journal of
Combinatorial Theory, Series B 67 (1996) 111–151]. Specifically, for any
k ≥ 3 there is a function ψk : (0, ∞) → [0, 1] such that for any d ∈ (0, ∞) \
{dk } the sequence (n−1 |Ck (G(n, d/n))|)n converges to ψk (d) in probability.
Furthermore, Pittel, Wormald and Spencer pointed out that a simple “branching
process” heuristic predicts the correct threshold and the correct size of the
k-core, and this argument has subsequently been turned into an alternative
proof of their result.
The aim of the present paper is to enhance this branching process perspective
of the k-core problem. Here we derive a multi-type branching process that
describes precisely how the k-core is “embedded” into the random graph for
any k ≥ 3 and any fixed average degree d = np > dk . This generalises prior
results on, e.g., the internal structure of the k-core. Indeed, in the physics
literature it was suggested to characterise the core by means of a “message
passing” algorithm called Warning Propagation. The Warning Propagation
description of the core will play a key role in the present paper.
This is joint work with Amin Coja-Oghlan, Oliver Cooley and Mihyun Kang.
Komplexität messen: Ein nützliches und interessantes Werkzeug für die
Zeitreihenanalyse – die ordinale Musterverteilung
Inga Stolz (Universität zu Lübeck)
Die Kolmogorow-Sinai-Entropie ist ein bekanntes Maß zur Komplexitätsmessung von dynamischen Systemen, sie zu berechnen ist jedoch nicht einfach. Die Wissenschaftler Band und Pompe erfanden kürzlich das Konzept
38
der Permutationsentropie, welche, wie sich herausgestellt hat, eng mit der
Kolmogorow-Sinai-Entropie verbunden ist. Dieses Maß nutzt aus, dass in
den Auf und Abs einer Messung viel Information über das zugrunde liegende
System gespeichert ist. In der ordinalen Zeitreihenanalyse werden diese Auf
und Abs durch sogenannte ordinale Muster beschrieben und ihre Verteilungen
ausgewertet.
Das Ziel dieses Vortrages ist es, die Methode der ordinalen Muster in der
Zeitreihenanalyse vorzustellen, Abwandlungen und deren Auswirkungen auf
die Beziehung zur Kolmogorow-Sinai-Entropie zu diskutieren sowie experimentelle Daten (im Besonderen EEG-Daten) in diesem Zusammenhang zu
beleuchten.
Polynomial Preserving Jump-Diffusions on the Unit Interval
Sara Svaluto-Ferro (Eidgenössische Technische Hochschule Zürich)
We present the class of polynomial preserving processes, which contains several important processes such as affine processes or processes with quadratic
diffusion coefficients. Processes in this class have the property that the calculation of (mixed) moments only requires the computation of matrix exponentials.
A polynomial preserving process can be defined as the solution to a martingale
problem whose operator is polynomial preserving, namely maps any polynomial to a polynomial of the same or lower degree. Choosing the unit interval as
state space, we characterize those polynomial preserving operators for which
the existence of a solution to the martingale problem is guaranteed.
Mean-square stiffness analysis of stochastic differential equations
Andreas Thalhammer (Johannes Kepler Universität Linz)
Whereas the concept of stiffness of deterministic problems is well-examined,
the notion of stiffness for stochastic differential equations (SDEs) has not been
treated in detail yet. A reliable characterisation of stiffness in the stochastic
setting is of great importance in practice, particularly if we are dealing with
problems where a necessary reduction of time step sizes for explicit methods
leads to significantly higher computational cost.
In this talk, we provide an overview of existing approaches to characterise
stiffness for deterministic and stochastic problems. Furthermore, we extend
a recently developed concept of stiffness for deterministic differential equations to the stochastic setting and link the proposed notion of stiffness in the
mean-square sense with results from the stability theory of linear stochastic
39
differential equations. Using these results, we conclude the talk by presenting numerical experiments with linear systems of SDEs coming from spatial
discretisation schemes for stochastic partial differential equations.
Analyse zeitdynamischer onkologischer Daten in Abwesenheit eines Ereignisses in der interessierenden Ereigniskategorie
Maria Umlauft (Universität Ulm)
In diesem Vortrag sollen verschiedene Methoden zur Analyse von Überlebenszeitdaten unter dem besonderen Umstand eines nicht beobachteten Ereignisses
in einer Ereigniskategorie vorgestellt werden. Die vorliegenden Daten stammen aus einer Kohortenstudie und enthalten Beobachtungen von Patienten,
welche an einem neuroendokrinen Tumor erkrankt sind. In Folge dessen wurden sie mit verschiedenen Radiopeptidtherapien behandelt, deren Einfluss
auf die Diabetesinzidenz untersucht werden soll. Eine Besonderheit für die
Analyse der vorliegenden Daten ist die Notwendigkeit einer Zuhilfenahme
von konkurrierenden Risiken-Modellen. Die sonst standardmäßig angewandte
Cox-Regression liefert im Fall eines nicht beobachteten Ereignisses auf Grund
der multiplikativen Intentitätsstruktur keine zufriedenstellenden Ergebnisse.
Die Herausforderung liegt damit in der Auswahl geeigneter Methoden, welche
in diesem Vortrag beschrieben und untereinander mit Hilfe einer Simulationsstudie verglichen werden sollen.
Smooth Densities for Rough Differential Equations on Manifolds
Martin Weidner (Imperial College London)
We want to show the smoothness of the law of solutions of rough differential
equations on smooth manifolds where the driving noise is a suitable Gaussian process. The analogue result for vector space valued solutions has been
established recently. Furthermore, the situation on manifolds is quite well
understood if the driving noise is Brownian motion. We aim at combining
these results while paying particular attention to whether additional structures
on the manifold (such as a Riemannian metric) play a role.
This is work in progress.
40
Localised Conditional Autoregressive Expectile Model
Xiu Xu (Humboldt-Universität zu Berlin)
Localised conditional autoregressive expectile (CARE) model accounts for
time-varying parameters in tail risk modelling. Our technique strikes a balance
between parameter variability and the modelling bias resulting in potentially
varying parameter homogeneity interval lengths. Over this intervals one can
safely assume a parametric model in expectile estimation. Based on empirical
evidence at three stock markets between 2005-2014 we show that CARE
parameters vary over time and exhibit changing distributional properties. It
is recommended to use between 1 month and 1 year of data in expectile
modelling at any trading day.
41
5
Teilnehmerliste∗
Markus Ableidinger (Johannes Kepler Universität Linz)
Randolf Altmeyer (Humboldt-Universität zu Berlin)
Nikolay Baldin (Humboldt-Universität zu Berlin)
Daniel Bartl (Universität Konstanz)
Andre Beinrucker (Universität Potsdam)
Viktor Bengs (Philipps-Universität Marburg)
Jana Bielagk (Humboldt-Universität zu Berlin)
Todor Bilarev (Humboldt-Universität zu Berlin)
Laura Bittner (Bergische Universität Wuppertal)
Antoine Brault (Université de Lorraine)
Paul Breiding (Technische Universität Berlin)
Thomas Buder (Technische Universität Dresden)
Thomas Cayé (Eidgenössische Technische Hochschule Zürich)
Jamil Chaker (Universität Bielefeld)
Shi Chen (Humboldt-Universität zu Berlin)
Alberto Chiarini (Technische Universität Berlin)
Giovanni Conforti (Universität Potsdam)
Peter Czuppon (Albert-Ludwigs-Universität Freiburg)
Alexander Dalinger (Technische Universität Darmstadt)
Todor Dinev (Universität Trier)
Dennis Dobler (Universität Ulm)
Markus Doktor (Technische Universität Kaiserslautern)
Achim Dörre (Universität Rostock)
Karl Ewald (Technische Universität Wien)
Mark Feodoria (Christian-Albrechts-Universität Kiel)
Victor Nzengang Feunou (Humboldt-Universität zu Berlin)
Tobias Fissler (Universität Bern)
Gordon Frank (Universität Rostock)
Peter Frentrup (Humboldt-Universität zu Berlin)
Martin Friesen (Universität Bielefeld)
Daniel Gaigall (Leibniz Universität Hannover)
Julian Gerstenberg (Leibniz Universität Hannover)
Lukas Gonon (Eidgenössische Technische Hochschule Zürich)
Adrian Gonzalez (Technische Universität Berlin)
Paulwin Graewe (Humboldt-Universität zu Berlin)
Claus Griessler (Universität Wien)
Miryana Grigorova (Humboldt-Universität zu Berlin)
∗ Unvollständige
Teilnehmerliste entsprechend der Datenschutzerklärungen.
42
Philipp Gschoepf (Humboldt-Universität zu Berlin)
Lingqi Gu (Universität Wien)
Maurilio Gutzeit (Universität Potsdam)
Stefan Häfner (Universität Duisburg-Essen)
Simone Hermann (Technische Universität Dortmund)
Felix Hermann (Albert-Ludwigs-Universität Freiburg)
Samuel Hetterich (Goethe-Universität Frankfurt a.M.)
Imke Höfers (BTU Cottbus-Senftenberg)
Oliver Janke (Humboldt-Universität zu Berlin)
Klebert Kentia Tonleu (Humboldt-Universität zu Berlin)
Maike Klein (Friedrich-Schiller-Universität Jena)
Hakam Kondakji (BTU Cottbus-Senftenberg)
Benedikt Köpfer (Albert-Ludwigs-Universität Freiburg)
Jenny Krüger (Technische Universität Berlin)
Kai Kümmel (Friedrich-Schiller-Universität Jena)
Christoph Kustosz (Technische Universität Dortmund)
Matti Leimbach (Technische Universität Berlin)
Anna Leister (Philipps-Universität Marburg)
Claudine Leonhard (Universität zu Lübeck)
Jan-Erik Lübbers (Technische Universität Darmstadt)
Jens Lueddeckens (Martin-Luther-Universität Halle-Wittenberg)
Andreas Mändle (Carl von Ossietzky Universität Oldenburg)
Nadine Moch (Bergische Universität Wuppertal)
Marvin Müller (Technische Universität Dresden)
Alexandra Neamtu (Friedrich-Schiller-Universität Jena)
Andrea Nickel (Universität Bielefeld)
Timo Pfrommer (Universität Stuttgart)
David Prömel (Humboldt-Universität zu Berlin)
Tahirivonizaka Rahantamialisoa (Leibniz Universität Hannover)
Felicia Raßmann (Goethe Universität Frankfurt a.M.)
Jasmin Röder (Justus-Liebig-Universität Gießen)
Alexandros Saplaouras (Technische Universität Berlin)
Max Schneider (Universität Potsdam)
Florian Seib (Technische Universität Berlin)
Anton Shardin (BTU Cottbus-Senftenberg)
Tobias Siems (Universität Greifswald)
Kathrin Skubch (Goethe Universität Frankfurt a.M.)
Inga Stolz (Universität zu Lübeck)
Alexandra Suvorikova (Humboldt-Universität zu Berlin)
Sara Svaluto-Ferro (Eidgenössische Technische Hochschule Zürich)
43
Andreas Thalhammer (Johannes Kepler Universität Linz)
Maria Umlauft (Universität Ulm)
Moritz Voß (Technische Universität Berlin)
Martin Weidner (Imperial College London)
Korakot Wichitsa-Nguan (Universität Potsdam)
Xiu Xu (Humboldt-Universität zu Berlin)
Oleksandr Zadorozhnyi (Universität Potsdam)
Tobias Zwingmann (Philipps-Universität Marburg)
44
Bootsanlegestelle Reederei Winkler, Charlottenburger Ufer 1, 10587 Berlin
HU Berlin, Erwin Schrödinger-Zentrum, Rudower Chaussee 26, 12489 Berlin
TU Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin

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