| 具有分红、流动储备金和利率的风险模型的绝对破产 |
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| 引用本文： | 张 燕,赵培标.具有分红、流动储备金和利率的风险模型的绝对破产[J].经济数学,2016(2):15-22. |
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| 作者姓名： | 张 燕 赵培标 |
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| 作者单位： | 1. 解放军理工大学理学院，南京 210094; 南京理工大学理学院，南京 211101;2. 南京理工大学理学院,南京,211101 |
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| 摘 要： | 建立了阈值分红策略下具有流动储备金、投资利率和贷款利率的复合泊松风险模型.利用全概率公式和泰勒展式,推导出了该模型的Gerber-Shiu函数和绝对破产时刻的累积分红现值期望满足的积分-微分方程及边界条件,借助Volterra方程,给出了Gerber-Shiu函数的解析表达式.
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| 关 键 词： | 保险数学 Gerber-Shiu函数 积分-微分方程 分红 流动储备金 |
A Risk Model with Credit and Debit Interests, Liquid Reserves and Dividends Under Absolute Ruin |
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| ZHANG Yan,ZHAO Pei-biao.A Risk Model with Credit and Debit Interests, Liquid Reserves and Dividends Under Absolute Ruin[J].Mathematics in Economics,2016(2):15-22. |
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| Authors: | ZHANG Yan ZHAO Pei-biao |
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| Institution: | (1. College of Science, PLA University of Science and Technology, Nanjing Jiangsu 211101, China; 2. School of Science, Nanjing University of Science and Technology, Nanjing Jiangsu 210094, China) |
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| Abstract: | This paper studied the compound Poisson risk model with liquid reserves ,credit interest and debit interest in the presence of a threshold dividend strategy .By the total law of probability and Taylor's expansion ,we first obtained the inte‐gro‐differential equations with boundary conditions satisfying the Gerber‐Shiu function and presented the closed form expres‐sions for the Gerber‐Shiu function .Secondly ,we derived the integro‐differential equations with boundary conditions satisfying the expected discounted present value of all dividends until absolute ruin by employing Volterra equations . |
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| Keywords: | insurance mathematics Gerber-Shiu function integro -differential equation dividend liquid reserves |
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