Optimal Proportional Reinsurance for Controlled Risk Process which is Perturbed by Diffusion

In this paper,we study optimal proportional reinsurance policy of an insurer with a risk processwhich is perturbed by a diffusion.We derive closed-form expressions for the policy and the value function,which are optimal in the sense of maximizing the expected utility in the jump-diffusion framework.We alsoobtain explicit expressions for the policy and the value function,which are optimal in the sense of maximizingthe expected utility or maximizing the survival probability in the diffusion approximation case.Some numericalexamples are presented,which show the impact of model parameters on the policy.We also compare the resultsunder the different criteria and different cases.