马氏调制费率复合Poisson-Geometric风险模型的预警区问题  

Duration of Negative Surplus for Compound Poisson-Geometric Risk Model with Markov-Modulated Premium Rates

作　　者：余国胜[1] 贺小丽[1] 姚春临[1] 熊昕 YU Guo-sheng HE Xiao-li YAO Chun-lin XIONG Xin(Schoolof Mathematics and Computer Science,Jianghan University,Wuhan 430056,Chin)

机构地区：[1]江汉大学数学与计算机科学学院,湖北武汉430056

出　　处：《经济数学》2016年第3期41-44,共4页Journal of Quantitative Economics

基　　金：武汉市市属高校教学研究项目(2015057)资助

摘　　要：考虑了一类具有马氏调制费率的复合Poisson-Geometric过程风险模型,充分利用盈余过程的强马氏性,得到第一个预警区的一个条件矩母函数所满足的微积分方程,并进一步在两状态情形下,当理赔额的分布为指数分布时得到了第一个预警区的一个条件矩母函数的具体表达式以解释结果.需要特别指出的是,所研究模型的盈余过程不具有平稳增量性,只能充分运用盈余过程的强马氏性,研究了一类具有马氏调制费率的复合Poisson-Geometric过程风险模型的预警区问题,丰富了保险公司对预警区问题的研究,对保险公司考虑财务预警系统以及保险监管部门设计某些监管指标系统具有一定的参考指导价值.The duration of negative surplus for compound Poisson-Geometric risk model with Markov-modulated premi- um rates is considered. By taking full advantage of the strong Markov property of the surplus process, an integral-differential e- quation of a conditional moment generating function for the first duration of negative surplus has been obtained. Under the two states model, when the claim is exponential distribution, the explicit expression of a conditional moment generating function for the first duration of negative surplus is given to illustrate the results. Particularly wish to point out, the surplus process of the research model is not stable and incremental, the strong Markov property of the surplus process can be fully used, the problem of the duration of negative surplus for compound Poisson-Geometric risk model with Markov-modulated premium rates is re- searched for the first time. It has enriched the insurance companies to the study of the duration of negative surplus. It has a cer- tain reference value to consider the financial early warning system for insurance companies and to design certain supervision in- dex system for insurance supervision department.

关 键 词：概率论与数理统计 条件矩母函数 微积分方程 马氏调制 预警区 复合Poisson-Geometric风险模型 

分 类 号：O211.6[理学—概率论与数理统计]