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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:
91B28Finance etc. (MSC2000)
49L20Dynamic programming method (infinite-dimensional problems)
60J65Brownian motion
93E20Optimal stochastic control (systems)