随机环境下具有阈值分红策略的风险过程的破产时间分析  

Analysis of the Ruin Time of Threshold Dividend Strategy Risk Model under Stochastic Environment

作　　者：温玉卓 唐胜达 邓国和 WEN Yuzhuo;,TANG Shengda;DENG Guohe(College of Economics and Management,Guangxi Normal University,Guilin Guangxi 541006,China;College of Mathematics and Statistics,Guangxi Normal University,Guilin Guangxi 541006,China)

机构地区：[1]广西师范大学经济管理学院,广西桂林541006 [2]广西师范大学数学与统计学院,广西桂林541006

出　　处：《广西师范大学学报（自然科学版）》2018年第3期56-62,共7页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(61761008);广西高校中青年教师基础能力提升项目(2018KY0051);广西人文社会科学发展研究中心项目(ZX2017006);广西自然科学基金(2016GXNSFBA380035);广西师范大学重点项目(2014ZD008);广西高校数学与统计模型重点实验室开放课题(2017GXKLM002)

摘　　要：本文提出随机环境下的阈值分红策略下PH索赔分布的风险过程,给出这一风险模型的破产时间Laplace-stieltjes变换(LST)解析式的一种新的求解方法。即,忽略风险过程的初始盈余,将其转化为相应的初始水平为0的有限的Markov流体队列(FMFQ)模型,应用FMFQ理论,根据风险过程的破产时间与对应FMFQ忙期的关系,得到风险过程破产时间的LST表示式,同时也推得最终破产概率的解析表示式。In this paper,a threshold dividend strategy risk model with phase-type claims under stochastic environment is analyzed and a novel algorithm to obtain the Laplace-stieltjes transform(LST)of the ruin time is proposed.The initial surplus of the risk process is neglected,and the risk process is transformed into a Finite Markov Fluid Queue(FMFQ)with initial level zero.Using the FMFQ theory,the LST expressions of the ruin time are obtained through the relationship between the ruin time of the risk process and the busy period of the FMFQ,and the expression of ultimate ruin probability is also presented.

关 键 词：风险理论 破产时间 LAPLACE-STIELTJES变换 有限Markov流体队列 

分 类 号：O211.9[理学—概率论与数理统计]