| 带干扰的MAP风险过程的期望贴现惩罚函数 |
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| 引用本文： | 唐胜达,秦永松. 带干扰的MAP风险过程的期望贴现惩罚函数[J]. 广西师范大学学报(自然科学版), 2011, 29(3): 23-27 |
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| 作者姓名： | 唐胜达 秦永松 |
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| 作者单位： | 广西师范大学数学科学学院,广西桂林,541004 |
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| 基金项目： | 国家自然科学基金资助项目(10971038); 广西教育厅科研资助项目(201106LX067) |
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| 摘 要： | 本文讨论了索赔到达过程为一般Markov点过程,即考虑索赔到达为MAP过程的一类带干扰的风险模型,给出了期望贴现惩罚函数的Laplace变换满足的积分-微分方程,对于Laplace变换为有理函数的索赔分布,采用差分变换方法,利用Dickson-Hipp算子,本文得到了期望贴现惩罚函数的简洁表达式.
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| 关 键 词： | 风险过程 期望贴现惩罚函数 MAP过程 积分-微分方程 Laplace变换 |
Gerber-Shiu Function of MAP Risk Process Perturbed by Diffusion |
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| TANG Sheng-da,QIN Yong-song. Gerber-Shiu Function of MAP Risk Process Perturbed by Diffusion[J]. Journal of Guangxi Normal University(Natural Science Edition), 2011, 29(3): 23-27 |
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| Authors: | TANG Sheng-da QIN Yong-song |
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| Affiliation: | TANG Sheng-da,QIN Yong-song(College of Mathematical Science,Guangxi Normal University,Guilin Guangxi 541004,China) |
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| Abstract: | A risk model perturbed by diffusion is proposed in this paper.Claims arrival belongs to markovian arrival process(MAP).The integro-differential equations satisfied by Laplace transform of the Gerber-Shiu functions and closed form of expression for the Gerber-Shiu functions are obtained through divided difference and Dickson-Hipp operator when the claim amount distribution is from the rational family.Finally,in order to illustrate the main results,a numerical example is provided. |
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| Keywords: | risk theory Gerber-Shiu function MAP Integro-differential equation Laplace transform |
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