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

作　　者：聂高琴[1] 刘次华[2] 

机构地区：[1]首都经济贸易大学统计学院,北京100070 [2]华中科技大学数学与统计学院,湖北武汉430074

出　　处：《数学的实践与认识》2011年第19期199-205,共7页Mathematics in Practice and Theory

基　　金：北京市属高等学校人才强教计划资助项目--中青年骨干人才培养计划资助;北京市教委统计学特色专业建设项目资助

摘　　要：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.

关 键 词：红利 罚金折现期望 混合分布 LAPLACE变换 

分 类 号：O211.67[理学—概率论与数理统计]