Optimal insurance demand under marked point processes shocks

• 成果类型: Article
• 署名作者: Touzi, N
• 署名单位: Universite PSL; Universite Paris-Dauphine; Institut Polytechnique de Paris; ENSAE Paris
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/aoap/1019737674
• 发表日期: 2000
• 页码: 283-312
• 关键词: OPTIMAL CONSUMPTION; incomplete market; martingale; portfolio; investor

摘要

We study the stochastic control problem of maximizing expected utility from terminal wealth, when the wealth process is subject to shocks produced by a general marked point process; the problem of the agent is to derive the optimal allocation of his wealth between investments in a nonrisky asset and in a (costly) insurance strategy which allows lowering the level of the shocks. The agent's optimization problem is related to a suitable dual stochastic control problem in which the constraint on the insurance strategy disappears. We establish a general existence result for the dual problem as well as the duality between both problems. We conclude by some applications in the context of power (and logarithmic) utility functions and linear insurance premium which show, in particular, the existence of two critical values for the insurance premium: below the lower critical value, agents prefer to be completely insured, whereas above the upper critical value they take no insurance.