阈红利边界下Erlang(2)风险过程的罚金折现期望函数(英文)

THE EXPECTED DISCOUNTED PENALTY FUNCTION FOR ERLANG(2) RISK PROCESS WITH A THRESHOLD DIVIDEND STRATEGY

本文研究了阈红利边界下Erlang(2)风险过程的罚金折现期望函数.利用算子变换及复合几何分布函数得到了罚金折现期望函数满足的微分积分方程,并给出了罚金折现期望函数解析表达式.

In this article,we consider the expected discounted penalty function for a risk process with a two-step premium rate in which the inter-claim times are Erlang（2） distributed. By operator transform and compound geometric distribution,we derive two integro-differential equations and two renewal equations for the expected discounted penalty function,and obtain the analytical expression for the expected discounted penalty function.