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
- 49L20 Dynamic programming method
- 49L25 Viscosity solutions
- 65N06 Finite difference methods

**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