马氏相依风险模型红利折现的矩

Moments of the Discounted Dividends and Related Problems in a Markov-dependent Risk Model

该文讨论常数红利边界下的马氏相依模型的矩的问题.首先,推导出破产前全部红利的折现期望、红利折现的高阶矩所满足的积分-微分方程组及相应的边界条件.然后,通过构造特殊的初始条件,利用Laplace变换,在给定的一类索赔分布下,得到上面方程组的显式解.最后,给出两状态下指数索赔的数值计算结果.

In this paper,a Markov-dependent risk model with a constant dividend barrier is considered.A system of integro-differentiai equations with boundary conditions satisfied by the expected present value of the total dividends prior to ruin and the moments of the discounted dividends,given the initial environment state,are derived and solved.In two-state model, explicit solutions to the integro-differential equations are obtained when claim size distributions are exponentially distributed.