| 马氏环境下带干扰Cox风险模型的罚金折现期望函数 |
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| 引用本文： | 刘向增,赵选民,田铮,张燕.马氏环境下带干扰Cox风险模型的罚金折现期望函数[J].数学的实践与认识,2007,37(14):189-196. |
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| 作者姓名： | 刘向增 赵选民 田铮 张燕 |
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| 作者单位： | 西北工业大学,应用数学系,陕西,西安,710072 |
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| 基金项目： | 国家自然科学基金;航空基础科学基金;陕西省自然科学基金 |
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| 摘 要： | 研究了马氏环境下带干扰的Cox风险模型.首先给出了罚金折现期望函数满足的积分方程,然后给出了破产概率,破产前瞬时盈余、破产赤字的分布及各阶矩所满足的积分方程.最后给出当索赔额服从指数分布且理赔强度为两状态时的破产概率的拉普拉斯变换.
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| 关 键 词： | Cox过程 罚金折现期望函数 积分方程 破产时刻 |
| 修稿时间： | 2007年1月18日 |
The Expected Discounted Penalty Function of Cox risk Process Perturbed by Diffusion in a Markovian Environment |
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| LIU Xiang-zeng,ZHAO Xuan-min,TIAN Zheng,ZHANG Yan.The Expected Discounted Penalty Function of Cox risk Process Perturbed by Diffusion in a Markovian Environment[J].Mathematics in Practice and Theory,2007,37(14):189-196. |
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| Authors: | LIU Xiang-zeng ZHAO Xuan-min TIAN Zheng ZHANG Yan |
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| Abstract: | We consider the Cox risk process perturbed by diffusion in a Markovian environment.First,we derive the integral equations satisfied by the expected discounted penalty function.Further,get the integral equations satisfied by the ruin probability,the moments and the distribution of the surplus immediately before the time of ruin and the deficit at ruin.Finally,we get the laplace transform of ruin probability when the claim sizes are exponent distribution and the claim intensity is two states. |
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| Keywords: | Cox process the expected discounted penalty function integral function the time of ruin |
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