Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
Abstract : This article deals with the problem of efficient insurance contracts under symmetric information and non Expected Utility in infinite dimension. We consider both the case of risk and the case of uncertainty. In the case of risk, we obtain two main results: The first one is that if the insurer is risk neutral, then for a large class of utility functions that need not be quasi-concave, efficient insurance contracts give complete coverage over a deductible. The second one is that if the insurer and the insured are both strictly strongly risk averse, then, even if there are other contingencies, efficient contracts depend only on the loss and are non decreasing, 1-lipschitz functions of the loss. Existence of efficient contracts thus follows without quasi-concavity hypotheses on utility functions. In the case of uncertainty, we first consider C.E.U maximizers with common capacity and concave utility index and show that the set of optimal contracts is the same as in the expected utility case. We then consider agents with epsilon-contaminated capacities of the same probability and concave utility index. We show that an optimal contract is such that for small losses, it is as if it was the optimal contract for expected utility maximizers with same utility index while for high losses, it is a contract which give complete coverage over a deductible.
DANA Rose-Anne, SHAHIDI Niousha
Université de PARIS - DAUPHINE
Place du Maréchal de Lattre De Tassigny - 75775 PARIS CEDEX 16 - FRANCE
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