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February 2000 Optimal insurance demand under marked point processes shocks
Nizar Touzi
Ann. Appl. Probab. 10(1): 283-312 (February 2000). DOI: 10.1214/aoap/1019737674


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.


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Nizar Touzi. "Optimal insurance demand under marked point processes shocks." Ann. Appl. Probab. 10 (1) 283 - 312, February 2000.


Published: February 2000
First available in Project Euclid: 25 April 2002

zbMATH: 1161.91419
MathSciNet: MR1765213
Digital Object Identifier: 10.1214/aoap/1019737674

Primary: 90A40 , 93E20
Secondary: 49N15 , 60H30 , 90A09

Keywords: convex analysis , Duality , Optimal insurance , optional decomposition , Stochastic control

Rights: Copyright © 2000 Institute of Mathematical Statistics


Vol.10 • No. 1 • February 2000
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