经典风险模型分红控制过程的最优停止问题

Optimal Stopping of the Classical Risk Model Controlled by Dividend Strategy

本文在带注资的经典风险模型的最优分红控制过程的基础上,进一步引入最优停止策略.目标是要找到最优的停止时刻,使得到该时刻为止,股东的折现分红与带有一定费用的折现注资二者之差的期望值最大化.通过建立值函数V（x）满足的HJB方程,我们找到了最优停止时刻τ~＊.特别的,当索赔服从指数分布时,通过计算最终得到了值函数V（x）和最优停止时刻.τ~＊的清晰表达式.

In this paper,based on the classical risk model with capital injection and controlled by optimal dividend strategy,we consider the optimal stopping strategy.The objective is to find the optimal stopping timeτ~＊,which maximizes the discounted value of the dividend payment minus the penalized discounted capital injection.Via the HJB equation satisfied by the value function V（x）,we find the optimal stopping timeτ~＊.In particular,in the case of exponential claim size,we give an explicit procedure to obtain the value function V（x） and the optimal stopping timeτ~＊.