| 带干扰的广义Erlang(n)风险模型破产前资产余额的最大值(英文) |
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| 引用本文： | 王姗姗,张春生.带干扰的广义Erlang(n)风险模型破产前资产余额的最大值(英文)[J].工程数学学报,2009,26(5). |
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| 作者姓名： | 王姗姗 张春生 |
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| 作者单位： | 南开大学数学科学学院,天津,300071 |
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| 基金项目： | The National Basic Research Program of China (973 Program) 2007CB814905; The Natural Science Foundation of China (10871102) |
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| 摘 要： | 破产前资产余额的最大值是反映保险公司资产实力的重要指标.随机误差因素改变了余额过程的轨道性质,以致于增加了研究上的本质困难.本文研究了带干扰的广义Erlang(n)风险模型破产前资产余额最大值的分布问题.我们推导出破产前资产余额的最大值满足具有一定边界条件的齐次积分微分方程.特别地,当索赔服从有理分布时,我们给出了精确结果.此外,与单纯的广义Erlang(n)风险模型相比较,我们的论证更为复杂结果更为精细,并且推广了那里的结果.
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| 关 键 词： | Sparre Andersen风险模型 广义Erlang(n)索赔间隔 破产前最大余额 扩散过程 积分一微分方程 |
The Maximum Surplus Before Ruin in the Generalized Erlang(n) Risk Model Perturbed by Diffusion |
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| WANG Shan-shan,ZHANG Chun-sheng.The Maximum Surplus Before Ruin in the Generalized Erlang(n) Risk Model Perturbed by Diffusion[J].Chinese Journal of Engineering Mathematics,2009,26(5). |
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| Authors: | WANG Shan-shan ZHANG Chun-sheng |
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| Affiliation: | WANG Shan-shan,ZHANG Chun-sheng (School of Mathematical Sciences,Nankai University,Tianjin 300071) |
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| Abstract: | The maximum surplus before ruin is an important index of assets in insurance institutions. Considering the important impact of random error factors on the nature of sample paths of the surplus process,which essentially increases diffculties in research,we investigate the distribution of the maximum surplus in generalized Erlang(n) risk model perturbed by diffusion in this paper. We derive a homogeneous integro-differential equation with certain boundary conditions,describing the maximum surplus. Particularl... |
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| Keywords: | Sparre Andersen risk process generalized Erlang(n) claim waiting time maximum sur-plus before ruin diffusion process integro-differential equation |
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