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Optimal investment for insurer with jump-diffusion risk process. (English) Zbl 1129.91020
Summary: We study optimal investment policies of an insurer with jump-diffusion risk process. Under the assumptions that the risk process is compound Poisson process perturbed by a standard Brownian motion and the insurer can invest in the money market and in a risky asset, we obtain the close form expression of the optimal policy when the utility function is exponential. We also study the insurer’s optimal policy for general objective function, a verification theorem is proved by using martingale optimality principle and Ito’s formula for jump-diffusion process. In the case of minimizing ruin probability, numerical methods and numerical results are presented for various claim-size distributions.

MSC:
91B30 Risk theory, insurance (MSC2010)
91G10 Portfolio theory
49L20 Dynamic programming in optimal control and differential games
60H30 Applications of stochastic analysis (to PDEs, etc.)
60J65 Brownian motion
93E20 Optimal stochastic control
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