一类混合分红策略下的广义Erlang(n)风险模型

A generalized Erlang(n) risk model with a hybrid dividend strategy

本文考虑混合分红策略下索赔来到间隔为广义Erlang(n)分布的更新风险模型,利用指数分布的无记忆性,分别得到破产前期望折现分红函数和折现分红的矩母函数满足的积分-微分方程及其边界条件.最后给出索赔为指数分布及索赔来到间隔为广义Erlang(2)分布的风险模型的期望折现分红函数的精确表达式.

In this paper, we consider the generalized Erlang（n） risk model with a hybrid dividend strategy.Using the lack-of-memory property of the exponential distribution, we derive integro-differential equations with boundary conditions satisfied by the expectation of the sum of discounted dividends until ruin and the moment generating function of the discounted dividend payments until ruin respectively. Explicit solutions of the expectation of the discounted dividend are given for a generalized Erlang（2） risk model and exponential-distributed claim amounts.