Optimal investment for insurer with jump-diffusion risk process

In this paper, 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.