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 proportional reinsurance contract: a dynamic programming duality approach

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Code(s) de Classification MSC:

Résumé: We study the optimal reinsurance strategy of an insurance company under proportional reinsurance contract. The objective of the insurance company is to maximize the expected utility of its reserve at some planning horizon and under a nonbankruptcy constraint. This optimization problem is related to a suitable dual stochastic control problem in which the delicate boundary constraints disappear. We characterize the dual value function as a viscosity solution of a variational inequality and we prove uniqueness result in the case of CRRA utility function. We characterize the optimal reinsurance strategy by the solution of the variational inequality. We solve it numerically by using an algorithm based on policy iterations.

Mots Clés: Optimal insurance ; stochastic control ; duality ; optional decomposition ; dynamic programming principle ; viscosity solution ; Howard algorithm

Date: 2002-10-16

Prépublication numéro: PMA-761