Université Paris 6
Pierre et Marie Curie
Université Paris 7
Denis Diderot

CNRS U.M.R. 7599
``Probabilités et Modèles Aléatoires''

Optimal risk control under excess of loss reinsurance


Code(s) de Classification MSC:

Résumé: We study the optimal reinsurance policy of an insurance company which gives part of its premium stream to another compagny in exchange of an obligation to support the difference between the amount of the claim and some retention level. This contract is known as excess of loss reinsurance. The objective of the insurance compagny is to maximize the expected utility of its reserve at some planning horizon and under a nonnegativity constraint. We suppose that reinsurance incurs a cost proportional to the size of risk run by the reinsurance compagny. \\ We first prove existence and uniqueness result for this optimization problem by using stochastic control methods. In a second part, we solve the associated Bellman equation numerically by using an algorithm based on policy iterations.

Mots Clés: Stochastic optimization ; state constraint ; dynamic programming principle ; viscosity solution ; Howard algorithm ; insurance

Date: 2001-10-25

Prépublication numéro: PMA-696

Postscript file : PMA-696.ps

Pdf file : PMA-696.pdf