Etude des marchés d'assurance non-vie à l'aide d'équilibres de ...

tel-00703797, version 2 - 7 Jun 2012
Chapitre 2. Theorie des jeux et cycles de marché
2.1 Introduction
Insurance market cycles and the study of their causes have been puzzling actuaries for
many years. Feldblum (2001) discusses four main causes that could explain the presence of
underwriting through their aggregate effect. These causes are (i) actuarial pricing procedure,
(ii) underwriting philosophy, (iii) interest rate fluctuations and (iv) competitive strategies. He
compares contributions through out the 20 th century on the topic, see also Markham (2007)
for an overview.
Actuarial pricing procedures are subject to claim cost uncertainty, information lag (due
to accouting, regulatory and legal standards). Such effects are likely to generate fluctuations
around an equilibrium price, when extrapolating premiums, see, e.g., Venezian (1985); Cummins
and Outreville (1987). In addition, a hard behavior of underwriters combined with a
lack of coordination is an extra recipe for underwriting cycles. In particular, price policies
cannot be sold independently of the market premium, but neither can the market premium be
driven by one’s individual actions. This is called underwriting philosophy by Feldblum (2001),
and is also noticed in Jablonowski (1985), who assumes (i) insurers do not make decisions in
isolation from other firms in the market, and (ii) profit maximization is not the exclusive,
or even the most important, motivation of insurers. Interest rate deviations further increase
the frequency and the amplitude of market cycles, as they have an impact on the investment
result and (indirectly) on the maximum rebate that underwriters can afford to keep presumably
low-risk customers. Fields and Venezian (1989) were among the first to demonstrate this
effect. Finally, the competition level on most mature insurance markets are such that any
increase in market share can only be carried out by price decrease ∗ (due to very little product
differentiation). Coupled with capital constraints (e.g. Gron (1994)) and price inelasticity,
insurers are forced not to deviate too much from market trends.
On a different level, basic economic models suggest that the equilibrium premium is the
marginal cost, as any upward deviation from this equilibrium will result in losing all the policies
in the next period. This theory would imply that all insurers price at the market premium
However, in practice customers do not move from a insurer to a cheaper insurer as swiftly
as economic models anticipate. There is an inertia of the insurance demand, preventing all
insured to shop arround for the cheapest insurer when their premium is slightly higher than the
market premium. So customer behavior is much more complicated. In addition to customer
loyalty, Feldblum (2001) points out that it is difficult for a new insurer to enter successfully
into the non-life insurance market.
More refined economic models focus on moral hazard and adverse selection. The celebrated
model of Rothschild and Stiglitz (see Rothschild and Stiglitz (1976)) deals with a utility-based
agent framework where insureds have private information on their own risk. Insurers provide
a menu of contracts (a pair of premium and deductible) and high-risk individuals choose
full coverage, whereas low-risk individuals are more attracted by partial coverage. Note that
the equilibrium price may not exist if all insurers offer just one type of contract. Picard
(2009) considers an extension by allowing insurers to offer participating contracts (such as
mutual-type contracts). This feature guarantees the existence of an equilibrium, which forces
(rational) insureds to reveal their risk level. An important source of applications of such
models is health insurance where moral hazard and adverse selection play a major role, see,
∗. The hunger for market share is driven by the resulting reduction of claim uncertainty is increasing the
policy number, which is motivated by the law of large numbers.
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