The Expected Discounted Penalty Function: From Infinite Time To Finite Time

主讲人 : 李栓明

In this paper we study the finite-time expected discounted penalty functions and their decompositions in the classical risk model perturbed by diffusion. We first give the solution to a class of second order partial integro-differential equation (PIDE) with certain boundary conditions. We show thatthe finite-time expected discounted penalty functions and their decompositions can be expressed in terms of the corresponding quantities under theinfinite-time horizon. We then find explicit  s for the finite timeruin probabilities and its decompositions: the finite-time ruin probability dueto oscillations and the finite-time ruin probability caused by a claim. Numerical examples are given when claims follow an exponential distribution.

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主讲人简介：

李栓明 (Shuanming Li)，墨尔本大学商学院精算中心副教授，博士生导师，墨尔本大学精算研究生教育与南开-墨尔本联合双硕士项目的负责人(Director of Master of Actuarial Science). 在精算，概率，统计，应用数学，运筹学，随机过程等刊物上发表论文50余篇。是50多国际期刊的审稿人, 美国数学评论的特约评论员。从2005至今，在墨尔本大学精算中心教授本科及研究生若干门，包括风险理论1，风险理论2，寿险数学1，寿险数学2，精算入门，随机过程在金融与保险中的应用，精算论文写作等；指导荣誉本科生与硕士20 余名，指导博士7名。