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

tel-00703797, version 2 - 7 Jun 2012
Chapitre 1. Sur la nécessité d’un modèle de marché
The two previous sections demonstrate that GLMs are easy to implement, but care on the
variable selection and appropriate data are needed to ensure reliable outputs. In this section,
we show how incorporating new key variables in the GLM regression substantially improves the
lapse rate predictions in the different premium scenarios. The rebate level partially reveals
the agent or the broker actions on the customer decisions, while the use of market proxies
illustrates how decisive the competition level is when studying customer price-sensitivity.
In conclusion, the GLM methodology, when used on appropriate data, fulfills the initial
objective to derive average lapse rate prediction taking into account individual features. Furthermore,
using the predicted lapse rate values of GLMs, it has been easy to identify customer
segments, which react differently to premium changes. The back-fit of the GLMs on the identified
populations is correct. At a customer segment level, GLMs provide a fair estimate of
lapse rate and price sensitivity for reasonable premium changes. But at a policy level, we
think lapse predictions should be treated carefully.
1.5 Testing asymmetry of information
Asymmetry of information occurs when two agents (say a buyer and a seller of insurance
policies) do not have access to the same amount of information. In such situations, one of
the two agents might take advantage of his additional information in the deal. Typically, two
problems can result from this asymmetry of information : adverse selection and moral hazard.
In insurance context, moral hazard can be observed when individuals behave in risker ways,
when they are insured. Insurers cannot control the policyholder’s actions to prevent risk.
Adverse selection depicts a different situation where the buyer of insurance coverage has a
better understanding and knowledge of the risk he will transfer to the insurer than the insurer
himself. Generally, the buyer will choose a deductible in his favor based on its own risk
assessment. Hence, high-risk individuals will have the tendency to choose lower deductibles.
Adverse selection is caused by hidden information, whereas moral hazard is caused by hidden
actions.
Joseph Stiglitz was awarded the Nobel price in economics in 2001 for his pioneer work
in asymmetric information modelling. In insurance context, Rothschild and Stiglitz (1976)
models the insurance market where individuals choose a “menu” (a couple of premium and
deductible) from the insurer offer set. Within this model, they show that high-risk individuals
choose contracts with more comprehensive coverage, whereas low-risk individuals will choose
higher deductibles.
1.5.1 Testing adverse selection
The topic is of interest when modelling customer behaviors, since a premium increase
in hard market cycle phase, i.e. an increasing premium trend, may lead to a higher loss
ratio. Indeed if we brutally increase the price for all the policies by 10%, most of high-risk
individuals will renew their contracts (in this extreme case), while the low-risk will just run
away. Therefore the claim cost will increase per unit of sold insurance cover.
In this paper, we follow the framework of Dionne et al. (2001), which uses GLMs to
test for the evidence of adverse selection ∗ . Let X be an exogenenous variable vector, Y an
∗. Similar works on this topic also consider the GLMs, see Chiappori and Salanié (2000) and Dardanoni
and Donni (2008).
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