基于MAP风险模型的最优分红问题研究  

Optimal Dividend-Payout in a MAP Risk Model

作　　者：陈旭[1] 杨向群[1] 

机构地区：[1]湖南师范大学数学与计算机学院,高性能计算与随机信息处理省部共建教育部重点实验室,长沙410081

出　　处：《数学物理学报（A辑）》2016年第1期176-186,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(11401204,11171101)资助~~

摘　　要：在保险公司财务核算和分红均发生在随机时间点的假设条件下,讨论保险公司的最优分红问题.假设保险公司的盈余过程是经过MAP(马氏到达过程)的相过程调制的复合泊松过程,保险公司对盈余过程的观测和分红都发生在MAP的跳点上,以最大化期望折现分红总量为目标,证明了最优分红策略为band策略,并分析了经济状态和分红机会对值函数和分红策略的影响.In this paper, we model the surplus process of the insurance by the classical com- pound Poisson risk model modulated by an continuous-time Markov chain, which is the phase process of a Markovian Arrival Process（MAP）. The surplus process can＇t be observed continu- ously. The observation and the possible dividend are restricted to a sequence of random discrete time points which are determined by the same MAP. The insurance has only observation oppor- tunities at some of these random time points, and has both observation and paying dividend opportunities at the other random time points. The object of the insurance is to select the dividend strategy that maximizes the expected total discounted dividend payments until ruin. The purpose of this paper is to analyze the impact of the paying dividend opportunity and the economic state on the value functions and dividend strategies. We show that the optimal dividend pay-out policy is a band policy at dividend pay-out times.

关 键 词：折现分红总量 随机观察 MAP 贝尔曼方程 

分 类 号：O211.9[理学—概率论与数理统计]