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

CNRS U.M.R. 7599
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``Probabilités et Modèles Aléatoires''
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**Auteur(s): **

**Code(s) de Classification MSC:**

- 93E20 Optimal stochastic control
- 90A09 Finance, portfolios, investment
- 49L25 Viscosity solutions
- 65N06 Finite difference methods

**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*