Optimal Dividend and Capital Injection Strategies in the Cramér-Lundberg Risk Model

الملخص EN

We discuss the optimal dividend and capital injection strategies in the Cramér-Lundberg risk model.

The value function V ( x ) is defined by maximizing the discounted value of the dividend payment minus the penalized discounted capital injection until the time of ruin.

It is shown that V ( x ) can be characterized by the Hamilton-Jacobi-Bellman equation.

We find the optimal dividend barrier b , the optimal upper capital injection barrier 0, and the optimal lower capital injection barrier - z * .

In the case of exponential claim size especially, we give an explicit procedure to obtain b , - z * , and the value function V ( x ) .