The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 10, Number 1 (2000), 283-312.
Optimal insurance demand under marked point processes shocks
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.
Ann. Appl. Probab., Volume 10, Number 1 (2000), 283-312.
First available in Project Euclid: 25 April 2002
Permanent link to this document
Digital Object Identifier
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
Touzi, Nizar. Optimal insurance demand under marked point processes shocks. Ann. Appl. Probab. 10 (2000), no. 1, 283--312. doi:10.1214/aoap/1019737674. https://projecteuclid.org/euclid.aoap/1019737674