一类索赔到达时间间距为混合分布的平均折现罚函数  

The Expected Discounted Penalty Function on a Class of the Claim Inter-arrival Times have Mixing Distributions

作　　者：江五元[1] 刘再明[1] 

机构地区：[1]中南大学数学学院,长沙410075

出　　处：《应用数学学报》2009年第4期757-765,共9页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(10371133)资助项目

摘　　要：本文考虑了索赔时间间距为指数分布与Erlang(2)分布混合时的平均折现罚函数,建立了该函数所满足的积分-微分方程及更新方程,讨论了其Laplace解。最后得出了破产概率所满足的Beekman卷积公式及索赔量分布分别为Phase-type分布和Pareto分布时破产概率的明确表达式和近似表达式。In this paper, we consider a compound renewal risk process in which the claim inter-arrival times are the mixture of exponentials and Erlang（2） distributions. A Integrodifferential equation and a renewal equation for the expected discounted penalty function are derived, and we also discuss the Laplace transform of the function. Finally, we obtain the Beekman＇s convolution formula for the ruin probability and the explict solution and the asymptotic one in the case where the individenal claim amount distribution is Phase-type and Pareto, respectively.

关 键 词：混合分布 平均折现罚函数 拉氏变换 更新方程 

分 类 号：O211.6[理学—概率论与数理统计]