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Insurance Contracts under Adverse Selection with Random Loss Severity

Dans l'analyse des problèmes d'antisélection en assurance, on suppose généralement que la richesse des individus est une variable aléqtoire binaire, selon que l'individu subit ou non une perte. Ceci interdit d'analyser la forme du contrat d'assurance partielle destiné aux individus à faible risque. Nous généralisons ici le modèle standard au cas où il y a plusieurs valeurs de perte, en considérant des distributions arbitraires sur un continuum de pertes. Nous montrons que l'espérance de perte est un critère suffisant pour identifier les catégories d'individus à risque faible et à risque élevé, de façon à reproduire les résultats de Rothschild et Stiglitz sur les marchés d'assurance concurrentiels. Nous montrons que la forme du contrat destiné aux individus à faible risque dépend de la nature de l'information révélée par le montant de la perte. Dans l'analyse de ce contrat, nous prenons également en considération la possibilité d'asymétries d'information ex post relativement aux états de perte. In the literature on adverse selection in insurance markets, it is usually assumed that the loss faced by individuals is single-valued. This precludes the analysis of the form of the incomplete coverage contract designed for the low-risk class. In the present paper, the two-type adverse selection model is extended to the case where the severity of the loss is random, by considering general distributions over a continuum of losses. We show that the expected value of the loss is sufficient to characterize the high and low risk types and to generalize Rothschild and Stiglitz' competitive market results. The form of the second-best contract for the low risks is shown to depend on the nature of the information revealed by the severity of the loss. In analyzing the form of this contract, we also allow for the possibility of ex post informational symmetries with respect to loss events.

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Paper provided by Université du Québec à Montréal, Département des sciences économiques in its series Cahiers de recherche du Département des sciences économiques, UQAM with number 9510.

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Date of creation: Sep 1995
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Handle: RePEc:cre:uqamwp:9510
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