考虑征税和利息的绝对破产的马氏调控风险模型  

On the Markov-modulated Insurance Risk Model with Interest,Debit Interest and Tax Payments

作　　者：王文元[1] 张爱丽[2] 胡亦钧[3] 明瑞星[4] 

机构地区：[1]新疆财经大学应用数学学院,乌鲁木齐830012 [2]南京审计大学数学与统计学院,南京211815 [3]武汉大学数学与统计学院,武汉430072 [4]浙江工商大学统计与数学学院,杭州310018

出　　处：《应用数学学报》2017年第2期240-266,共27页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(11401498;11661074);中央高校基本科研基金(20720140525);浙江省自然科学基金(LY16A010001);浙江省人文社科基地(统计学);浙江省教育厅基金(1020KZ0413455)资助项目

摘　　要：本文考虑马氏调控风险模型.在该模型中,当嵌入的马氏链的状态发生变化时,索赔达到的强度,索赔额的分布和征税的税率也随之发生改变.当盈余为正的时候,保险公司获得无风险投资收益,假定收益率是一正的常数;当盈余为负的时候,保险公司通过借贷来维持其业务,假定借贷利率也是一个正的常数.当保险公司的借贷利息大于保费收入的时候,保险公司就无法继续自己的业务,此时称保险公司绝对破产了.本文给出保险公司的生存概率,总赋税的现值,盈余从负变为零的概率(复苏概率)等特征量满足的解析式,并在一状态的马氏调控风险模型下得到了复苏概率的具体表达式.此外,在指数索赔下,将上述特征量通过数值的方法进行敏感性分析.In this paper we consider the Markov-modulated risk model in which the rate for the Poisson claim arrivals, the distribution for the claim amounts and the rate of tax vary in time depending on the state of an external Markov chain. The model also assumes that the insurer earns interest at a constant rate if the surplus is positive and pays out debit interest at another constant rate if the surplus is negative. Absolute ruin occurs at the moment the surplus first drops below a critical negative constant level. Analytical expressions of the non- absolute-ruin probability, the expected discounted tax payments as well as the probability of recovery are obtained. When the claims are exponentially distributed and there is only one state in the state space of the underlying Markov chain, explicit expression of the probability of recovery is also derived. Finally, for exponential claims, numerical comparison of the resulting non-absolute-ruin probabilities and discounted expected tax payments with Markov modulation, interest and debit interest to the case without are given.

关 键 词：马氏调控风险过程 生存概率 总赋税现值 复苏概率 

分 类 号：O211.9[理学—概率论与数理统计]