The Annals of Applied Probability

Optimal insurance demand under marked point processes shocks

Nizar Touzi

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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.

Article information

Ann. Appl. Probab., Volume 10, Number 1 (2000), 283-312.

First available in Project Euclid: 25 April 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 93E20: Optimal stochastic control 90A40
Secondary: 60H30: Applications of stochastic analysis (to PDE, etc.) 49N15: Duality theory 90A09

Optimal insurance stochastic control convex analysis duality optional decomposition


Touzi, Nizar. Optimal insurance demand under marked point processes shocks. Ann. Appl. Probab. 10 (2000), no. 1, 283--312. doi:10.1214/aoap/1019737674.

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