| 一类带利率的马氏风险模型 |
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| 引用本文： | 夏征,王春伟,杨万才.一类带利率的马氏风险模型[J].河南科技大学学报(自然科学版),2011,32(6):72-76,9. |
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| 作者姓名： | 夏征 王春伟 杨万才 |
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| 作者单位： | 河南科技大学数学与统计学院,河南,洛阳,471003 |
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| 基金项目： | 河南省基础与前沿技术研究计划项目，河南科技大学博士科研启动基金项目 |
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| 摘 要： | 考虑了带有常利率的马氏相依风险模型,保险公司的经营受到外部马氏环境的干扰更符合保险公司的实际经营状况。利用盈余过程的马氏性及随机微分方程得到了该模型期望折现罚金函数(Gerber-Sh iu函数)所满足的积分微分方程及边值条件,并运用Lap lace变换得到了外部环境只有两个状态并且索赔额服从指数分布时Gerber-Sh iu函数满足的积分方程。
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| 关 键 词： | Gerber-Shiu函数 马尔科夫过程 积分微分方程 破产概率 |
A Kind of Markovian Risk Model with Interest Rate |
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| XIA Zheng,WANG Chun-Wei,YANG Wan-Cai.A Kind of Markovian Risk Model with Interest Rate[J].Journal of Henan University of Science & Technology:Natural Science,2011,32(6):72-76,9. |
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| Authors: | XIA Zheng WANG Chun-Wei YANG Wan-Cai |
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| Institution: | (Mathematics & Statistics School,Henan University of Science & Technology,Luoyang 471003,China) |
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| Abstract: | This paper considers a Markov-dependent risk model with constant interest force,which accords with actual operating condition.By using Markov property of the surplus process and the theory of stochastic differential equation,the integro-differential equations satisfied by the expected discounted penalty function(also named Gerber-Shiu function) and the boundary conditions are obtained.When the claims obey exponential distribution and the state of the external Markovian environment is two-state,the integral equations satisfied by the Gerber-Shiu function are obtained. |
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| Keywords: | Gerber-Shiu function Markov process Integro-differential equation Probability of ruin |
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