On the Expected Discounted Penalty Function for a Risk Process with Stochastic Return on Investments  

作　　者：Li Li LI Jing Hal FENG Li Xin SONG 

机构地区：[1]School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China

出　　处：《Journal of Mathematical Research and Exposition》2010年第2期309-318,共10页数学研究与评论（英文版）

基　　金：Supported by Key Project of National Social Science Fund (Grant No.06&ZD039);"Mathematics+X" Project of DUT

摘　　要：This paper considers the expected discounted penalty function Φ（u） for the perturbed compound Poisson risk model with stochastic return on investments. After presenting an integro-differential equation that the expected discounted penalty function satisfies, the paper derives the closed form solution by constructing an identical equation. The exact expression for Φ （0） is given using the Laplace transform technique when interest rate is constant. Applications of the results are given to the ruin probability and moments of the deficit at ruin.This paper considers the expected discounted penalty function Φ（u） for the perturbed compound Poisson risk model with stochastic return on investments. After presenting an integro-differential equation that the expected discounted penalty function satisfies, the paper derives the closed form solution by constructing an identical equation. The exact expression for Φ （0） is given using the Laplace transform technique when interest rate is constant. Applications of the results are given to the ruin probability and moments of the deficit at ruin.

关 键 词：expected discounted penalty function integro-differential equation Laplace transform ruin. 

分 类 号：O211.67[理学—概率论与数理统计] TU311.3[理学—数学]