The Phase-type Risk Model Perturbed by Diffusion under a Threshold Dividend Strategy  

作　　者：Wu-yuan Jiang Zhou-jun Yang 

机构地区：[1]Department of Mathematics, Hunan Institute of Science and Technology [2]School of Finance and Statistics, Hunan University

出　　处：《Acta Mathematicae Applicatae Sinica》2013年第1期215-224,共10页应用数学学报（英文版）

基　　金：Supported by the National Natural Sciences Foundations of China (70971037 and 71171078);the Doctoral Fund of Ministry of Education of China (20100161110022);China Postdoctoral Science Foundation funded project(2012M521514);Hunan Postdoctoral Scientific Program of China (2012RS4030);the Sciences Foundations of Hunan Institute of Science and Technology of China (2012Y26);the aid program for Science and Technology Research Team in Higher Educational Institutions of Hunan Province of China

摘　　要：This paper considers a perturbed renewal risk process in which the inter-claim times have a phasetype distribution under a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generating function and the ruth moment of the present value of all dividends until ruin are derived. Explicit expressions for the expectation of the present value of all dividends until ruin are obtained when the claim amount distribution is from the rational family. Finally, we present an example.This paper considers a perturbed renewal risk process in which the inter-claim times have a phasetype distribution under a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generating function and the ruth moment of the present value of all dividends until ruin are derived. Explicit expressions for the expectation of the present value of all dividends until ruin are obtained when the claim amount distribution is from the rational family. Finally, we present an example.

关 键 词：DIFFUSION dividend payments threshold dividend strategy integro-differential equation rationalfamily Phase-type distribution 

分 类 号：F840[经济管理—保险] O211.67[理学—概率论与数理统计]