Stochastische Analysis und Stochastik der Finanzmärkte Strong rate

Humboldt-Universität zu Berlin
Institut für Mathematik
Technische Universität Berlin
Institut für Mathematik
Berlin Mathematical School
(BMS)
Einstein-Zentrum für Mathematik
Berlin(ECMath)
Im Rahmen des Forschungsseminares
Stochastische Analysis und
Stochastik der Finanzmärkte
spricht
Olivier Pamen
(University of Liverpool/AIMS Ghana)
zu dem Thema
Strong rate of convergence for the Euler-Maruyama
approximation of SDES with irregular drift coefficient
Zeit: Donnerstag, 17. November 2016, 16 Uhr c.t.
Ort: HU Berlin, Johann von Neumann - Haus, Rudower Chaussee 25, Hörsaal 1.115
Abstract: In this talk, we consider a numerical approximation of the stochastic differential equation
(SDE)
t
Z
b(s, Xs )ds + Lt , x0 ∈ Rd , t ∈ [0, T ],
Xt = x0 +
0
where b : [0, T ] × Rd → Rd is the drift coeffcient and the noise L = (Lt )0≤t≤T is a d-dimensional Lévy
process. In general, convergence of numerical methods are studied under the classical assumption that the
coeffcient of the SDE is globally Lipschitz continuous. However, this assumption is not always satis
ed for SDEs used in practice, this makes the global Lipschitz based idea not immediately applicable. We
assume that the drift b is Hölder continuous in both time and space variables. We provide the rate of
convergence for the Euler-Maruyama approximation when L is a Wiener process or a truncated symmetric
α- stable process with α ∈ (1, 2). Our technique is based on the regularity of the solution to the associated
Kolmogorov equation. Traditionally, the Kolmogorov equation is used to study the weak convergence rate
for the Euler-Maruyama approximation which is for example very important in
nancial applications.(This talk is based on a join work with Dai Taguchi, Ritsumeikan University.)
Kaffee und Tee ab 15.45 Uhr im Raum 1.214, Johann von Neumann - Haus,
Rudower Chaussee 25
Interessenten sind herzlich eingeladen!
Prof. P. Bank
Prof. P. Friz
Prof. U. Küchler
Prof. D. Becherer
Prof. U. Horst
Prof. A. Papapantoleon
Prof. H. Föllmer
Prof. P. Imkeller
Prof. N. Perkowski

Download Report