What are insurance captives

What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
Optimal risk financing in large corporations
through insurance captives
Pierre Picard1 and Jean Pinquet2
2
1
Ecole Polytechnique
Paris 10 & Ecole Polytechnique
2012, September 6, Lausanne
EAJ Conference
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
What are insurance captives ?
A captive is an insurance or reinsurance company established by
a parent group to manage its own risks.
The parent group: a large company, with business units throughout the world.
Captives organize self-insurance at the group level rather than at
the business unit level in order to increase risk retention capacity.
Captives rely on inter-individual (business units) diversification of
risks, whereas finite risk solutions are self insurance arrangements
relying on inter-temporal diversification.
Captives: loss reserving presented as insurance.
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
What are insurance captives ?
Captives insure property-liability lines (third party liability, property damage, business interruption), and also social liabilities (employee benefits) in the US.
The growth of the captive industry began in the 1960s and the
move by parent companies to establish their captives offshore
(Bermuda...).
The 1970s and the 1980s were a period of tremendous growth of
the captive industry (lack of liability coverage, tax reasons...)
In 2009 : 5,290 captives in the world (Business Insurance’s annual
captive survey)
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
Number of captives
5600
Figure 1: recent growth in captives
5400
5200
5000
4800
4600
4400
4200
4000
2001
2002
2003
2004
2005
2006
2007
Source: Business Insurance
Insurance captives
2008
2009
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
Reasons for captive arrangements that are not
addressed by the paper
Tax reasons: loss reserving presented as insurance, in order to
use tax deductibility for insurance premiums and a timing gain,
which can be important for liability lines.
Depending on the environment, captives must transfer a given
proportion of risk or accept risks from outside the parent group
(”rent a captive” arrangement) in order to obtain tax deductibility
of premiums.
Information issues: monitoring of prevention activities in the business units by the risk manager of the parent company (peer effects
on business units managers), disclosure of technical results in order to get better prices on insurance programs.
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
A reinsurance captive scheme
Holding
company
Risk transfer
in upper layers
Business
unit #1
Parent
company
Insurance
purchase (risk
transferred above
a deductible)
Other reinsurance
companies
Retrocession
Fronting
Insurance
Company
Massive risk transfer
in a lower layer
Monitoring of
rating and claim
handling
Reinsurance
Captive (and
risk manager)
For all the business units:
Monitoring of prevention
activities, results disclosure
and competition between
peers
Business
unit #k
Consolidation of accounts
A real-world reinsurance captive arrangement
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
Stylized facts
Captives = Internal risk pooling between the business units of the
parent group + risk transfer toward the reinsurance market.
Cessions are targeted at lower risk layers and insurance or reinsurance captives cede or retrocede the higher layers to reinsurance
markets.
Discretionary use of captives?
Captives’ activity reacts to the insurance underwriting cycle (Example : the 1984-1986 hard market cycle for liability lines), and
to wealth effects (Example: in 2009 many parent companies have
tapped their captives to enhance corporate capital).
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
Objectives of the paper
We analyze captives from an optimal insurance contract perspective, and especially the vertical contractual chain that may take
several form, in particular :
business units −→ fronters −→ reinsurance captives −→ reinsurers
How does this vertical chain acts as an expansion tank of the
parent group’s self insurance capacity, in reaction to price and
wealth effects?
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
Outline of the presentation
1
Optimal insurance captive schemes
2
Fronting and reinsurance captives
3
Conclusion
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
The model
A corporation organized as a holding company: business units
i = 1, ..., n.
Πi = initial endowment and cash-flows of unit i during the current
period.
Reasons for avoiding low values of Πi : unit i may have to call up
external capital or to delay profitable investment projects, hence
additional costs and lower profits.
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
The objective function
The shareholder value is
 n

X


W = E 
Bi (Πi ) ,
i=0
where the Πi may include an additive independent background
risk, and where B0i > 0, B00
< 0, (i = 0, . . . , n).
i
The Bi provide a rationale for stabilizing the short-term income
(usual reasons invoked to withdraw from risk neutrality: convexity of tax schedules, or the to Froot, Scharfstein and Stein
arguments, i.e. decreasing returns on investments + increasing
marginal cost of external financing).
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
An insurance captive scheme
Reinsurer
T (t1 ,  , t n )
Q
Local insurer of
Business unit i
Ii (~
xi )
Insurance
captive
ki
Pi
Business unit i
(i ∈ Al )
~
xi
Soft market period
Π0
ti ( ~
xi )
ki
Business unit i
Πi
(i ∈ Ac )
Hard market period
Figure 1: insurance captive
Insurance captives
Πi
~
xi
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
Comments and results (I)
The objective function is decentralized between the holding and
the business units, but the variables (fees payed to the insurance
captive, compensation policy, reinsurance plan) are controlled by
the holding company.
The business unit transfers all the risks to the captive if prices of
the local insurer are large enough (hard market).
Optimal compensations: of the Arrow type (Ii (xi ) = (xi − d0i )+ ) for
business units insured by a local insurer.
For a business unit insured by the captive, the marginal compensation is equal to zero below a deductible, then comprised between
0 and 1. The reinsurance contract is of the stop-loss type.
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
Comments (II)
The transfer between the captive and the business unit equalizes
the expected marginal value of cash in the business unit and in
the captive.
The captive can also act as a reinsurer, and compensates fronters
rather than business units. The reinsurance captive may also cede
risks to a retrocessionnaire.
The following figure summarizes the reinsurance captive arrangement.
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
A reinsurance captive scheme
Retrocessionnaire
T (C1 ,  , Cn )
Q
Reinsurance
captive
Ci ( I i ( ~
xi ))
Ki
Ii (~
xi )
Business unit i
~
xi
Fronting insurer
of business unit i
Pi
Figure 2: reinsurance captive
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
Results
Proposition: an optimal reinsurance captive scheme is defined by two
deductible levels d0i , d1i and a threshold Ii∗ such that
Ci (Ii ) = min(Ii , Ii∗ )
0
0
Ii (x) ≡ 0 if x < d0i ; 0 < Ii (x) < 1 if d0i < x < d1i + Ii∗ ;
0
Ii (x) ≡ 1 if d1i + Ii∗ < x.
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
Optimal compensation schemes (if piecewise linear)
Ii
*
Ii
Ci
45°
*
Ii
0
0
di
1
di
1
*
xi
di+Ii
Figure 3
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
Conclusions (1)
Reinsurance captives dominate insurance captives when standard
direct insurers have lower claims handling and underwriting costs
than captives (soft market): lower costs of the fronters + the risk
sharing optimality of an umbrella policy offered by retrocessionnaires.
With captives, the optimal insurance of decentralized business
units involves deductible insurance contracts with partial coverage at the margin (optimal risk sharing between the business units
and the captive).
Insurance captives
What are insurance captives ? Optimal insurance captive schemes Fronting and reinsurance captives Conclusion
Conclusions (2)
Fronters fully cede their risks to the reinsurance captive up to a
certain limit. Partial cessions above this limit are optimal under
increasing marginal cost of capital. The reinsurance captive retrocedes its risk to the reinsurance market through a stop-loss contract, thereby offering an umbrella insurance policy to the holding
company.
The optimal insurance coverage as well as the optimal cession
and retrocession operations depend on price parameters, and particularly on the capital cost of local insurers and on the loading
factor of retrocessionnaires, as well as on initial endowments of
the business units. Variations across time of these cost and wealth
parameters affect the attractivity of captive arrangements.
Insurance captives

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