考虑随机观察时间的马尔可夫到达风险模型的分红问题

近年来分红策略下的风险模型成为风险理论的研究热点之一。本项目拟研究带随机观察时间的马尔可夫到达风险模型的分红问题，主要内容包括：(1)考虑观察时间为指数分布的障碍分红策略下的马尔可夫到达风险模型，讨论Gerber-Shiu折现罚函数和累积分红折现均值满足的积分微分方程及其解，并研究索赔额属于次指数分布族S时相应的渐进公式；(2)考虑观察时间为Erlang(n)分布的障碍分红策略下的马尔可夫到达风险模型，讨论Gerber-Shiu折现罚函数和累积分红折现均值满足的积分微分方程及其解，并研究索赔额属于次指数分布族S时相应的渐进公式；(3)分别考虑观察时间为指数分布和Erlang(n)分布的障碍分红策略下带扰动的马尔可夫到达风险模型，讨论Gerber-Shiu折现罚函数和累积分红折现均值满足的积分微分方程及其解，并研究索赔额属于次指数分布族S时相应的渐进公式。

The risk model with dividend strategy has become one of the hot topics in risk theory. The project consider dividend problems in risk model where claims arrive according to a Markovian arrive process, the main contents include: (1)We consider a MAP risk model with exponentially distributed observation time under barrier strategy, and we will derive and solve the integro-differential equations for the Gerber-Shiu expected discounted penalty function and the total dividend payments, then we present some asymptotic formulas for the Gerber-Shiu expected discounted penalty function and the total dividend payments until ruin when the claim size is subexponential distribution of S; (2)We consider a MAP risk model with Erlang(n) distributed observation time under barrier strategy, and we will derive and solve the integro-differential equations for the Gerber-Shiu expected discounted penalty function and the total dividend payments, then we present some asymptotic formulas for the Gerber-Shiu expected discounted penalty function and the total dividend payments when the claims size is subexponential distribution of S; (3)We consider dividend problems on the perturbed MAP risk model under exponentially distributed observation time or Erlang(n) distributed separately, and then we will derive and solve the integro-differential equations for the Gerber-Shiu expected discounted penalty function and the total dividend payments, and then present some asymptotic formulas for the Gerber-Shiu expected discounted penalty function and the total dividend payments when the claim size is subexponential distribution of S.