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abstract: 'We study the stochastic control problem of maximizing expected utility from terminal wealth under a non-bankruptcy constraint. The wealth process is subject to shocks produced by a general marked point process. The problem of the agent is to derive the optimal insurance strategy which allows “lowering” the level of the shocks. 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 the unique viscosity solution of the corresponding a Hamilton Jacobi Bellman Variational Inequality (HJBVI in short).'
author:
- |
    Mohamed MNIF\
    LAMSIN\
    Ecole Nationale d’Ingénieurs de Tunis\
    B.P. 37, 1002, Tunis Belvédère, Tunisie\
    mohamed.mnif@enit.rnu.tn
date: 'August 18, 2010'
title: 'Optimal insurance demand under marked point processes shocks: a dynamic programming duality approach'
---

[**Key words :**]{} Optimal insurance; stochastic control; duality; optional decomposition; dynamic programming principle; viscosity solution

[**MSC Classification (2000) :**]{} 93E20, 60J75, 49L25.

Introduction
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We study the optimal insurance demand problem of an agent whose wealth is subject to shocks produced by some marked point process. Such a problem was formulated by Bryis [@bri86] in continuous-time with Poisson shocks. Gollier [@gol94] studied a similar problem where shocks are 