Optimal dividend payout for classical risk model with risk constraint

In this paper we consider the problem of maximizing the total discounted utility of dividend payments for a Cramér-Lundberg risk model subject to both proportional and fixed transaction costs. We assume that dividend payments are prohibited unless the surplus of insurance company has reached a level b. Given fixed level b, we derive a integro-differential equation satisfied by the value function. By solving this equation we obtain the analytical solutions of the value function and the optimal dividend strategy when claims are exponentially distributed. Finally we show how the threshold b can be determined so that the expected ruin time is not less than some T. Also, numerical examples are presented to illustrate our results.