常数红利下索赔到达时间间距为混合分布的罚金折现期望函数

Expected Discounted Penalty Function for the Claim Inter-Arrival Times Have Mixing Distributions with Constant Dividend Barrier

在常数红利策略下考虑索赔时间间隔为指数分布与Erlang(2)分布混合时的风险模型,在此红利策略下,若保险公司的盈余在红利线以下时不支付红利,否则红利以等于保费率的常速率予以支付.对于此风险模型,推导并求解了罚金折现期望函数所满足的微积分方程,并在索赔量为指数分布时研究了其解的形式.

We consider the risk model in the presence of a constant dividend barrier in which the claim inter-arrival times are the mixture of exponential and Erlang（z） distributions. Under such as strategy, no dividends are paid if the insurer＇s surplus is below the dividend level. Otherwise, dividends are paid at a constant rate that is equal to the premium rate. For this risk model, An integro-differential equation satisfied by the expected discounted penalty function is derived and solved. And, the form of its solution is studied when the claim size is exponentially distributed.