逐段决定复合泊松风险模型的最优分红与注资策略

Optimal dividend and capital injection strategies in the piecewise-deterministic compound Poisson risk model

研究了逐段决定复合泊松风险模型的最优分红和注资问题,以股东的破产时刻折现分红减去惩罚折现注资的差的期望值最大化为目标,通过求解相应的HJB方程,得到了对应的值函数,进而得出最优分红和注资策略是Threshold策略的结论,使风险模型更加符合实际,更具现实意义.

Optimal dividend payments and capital injections of the piecewise-deterministic compound Poisson risk model were discussed. The objective of an insurance business under consideration was to maximize the discounted dividend payments minus the penalized discounted capital injections. By a method to determine numerically the solution to the HJB equation,the corresponding Hamilton-Jacobi-Bellman equation was derived. And the optimal dividend and strategy was the Threshold strategy. This conclusion made the risk model have more realistic and more practical significance.