考虑征税和利息的绝对破产的马氏调控风险模型

发布时间：2018-06-08 10:51

本文选题：马氏调控风险过程 + 生存概率　；参考：《应用数学学报》2017年02期

【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.
[Abstract]:In this paper, we consider the Markov regulatory risk model. In this model, when the state of the embedded Markov chain changes, the strength of the claim, the distribution of the claim amount and the tax rate of the tax will also change. When the surplus is positive, the insurance company obtains a risk-free investment return, assuming that the yield is a positive constant; when the surplus is negative, the insurance company maintains its business by borrowing, assuming that the borrowing rate is also a positive constant. Insurance companies are unable to continue their business when the interest on their loans exceeds premium income, saying the insurance company is absolutely bankrupt. In this paper, we give the analytic expressions of the survival probability of insurance company, the present value of total tax, the probability of surplus from negative to zero (recovery probability), and obtain the concrete expression of recovery probability under the Markov risk model of one state. In addition, the sensitivity analysis of the above characteristics is carried out by numerical method under exponential claims.
【作者单位】：新疆财经大学应用数学学院;南京审计大学数学与统计学院;武汉大学数学与统计学院;浙江工商大学统计与数学学院;
【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
【分类号】：O211.67

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