考虑征税和利息的绝对破产的马氏调控风险模型

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考虑征税和利息的绝对破产的马氏调控风险模型王文元¹, 张爱丽², 胡亦钧³, 明瑞星⁴1. 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 On the Markov-modulated Insurance Risk Model with Interest, Debit Interest and Tax Payments WANG Wenyuan¹, ZHANG Aili², HU Yijun³, MING Ruixing⁴1. School of Applied Mathematics, Xinjiang University of Finance and Economics, Urumqi 830012, China;
2. School of Mathematics and Statistics, Nanjing Audit University, Nanjing 211815, China;
3. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;
4. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China

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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.

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收稿日期: 2013-03-04

PACS:

O211.9

基金资助: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）和浙江省教育厅基金（1020KZ0413455）资助项目

引用本文:

王文元, 张爱丽, 胡亦钧, 明瑞星. 考虑征税和利息的绝对破产的马氏调控风险模型[J]. 应用数学学报, 2017, 40(2): 240-266. WANG Wenyuan, ZHANG Aili, HU Yijun, MING Ruixing. On the Markov-modulated Insurance Risk Model with Interest, Debit Interest and Tax Payments. Acta Mathematicae Applicatae Sinica, 2017, 40(2): 240-266.

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