带有Markov链利率的相依风险模型破产概率的界  

Bounds for Ruin Probability in a Dependent Risk Model with a Markov Chain Interest Rate

作　　者：吕海娟[1] 张基培 张晋源[1] 彭江艳[1] 

机构地区：[1]电子科技大学数学科学学院,成都611731

出　　处：《重庆师范大学学报（自然科学版）》2017年第3期69-72,共4页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金(No.71501025);中国博士后科学基金第57批面上资助项目(No.2015M572467);四川省应用基础研究项目(No.2016JY0257)

摘　　要：【目的】研究具有齐次马氏链利率过程的离散时间相依风险模型。【方法】针对保费在期初收取和索赔在期末收取的情况,利用鞅方法和更新迭代的方法对破产概率模型进行研究,其中利率的马尔可夫性体现了未来利率与历史利率的独立性,保费过程和索赔过程都具有高阶自回归结构,考虑两者各自的相依性可使模型更具有普遍性。【结果】得到了所研究风险模型破产概率的上界。【结论】研究结果为解决实际生活中的保险问题提供了一定的理论依据。[Purposes]It investigates a discrete time dependent risk model where the interest rate process is homogeneous Markov chain, [Methods]The premiums are received at the beginning of each period and the claims are obtained at the end of each period in the model, the model was studied by using martingale method and renewal the iterative method. The Markov chain interest reflects the independence of the further rates and historic rates. The premiums process and the claims process have higher-order autoregressive structure. It can make the model more universal to consider their dependence. [Findings]The upper bound of infinite time ruin probabilities derived by using martingale method and renewal the iterative method. [Conclusions] The results provide certain theoretical base for the insurance problem in real life.

关 键 词：MARKOV链 高阶自回归结构 离散时间风险模型 破产概率 鞅方法 

分 类 号：O211.9[理学—概率论与数理统计]