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)  

The Maximum Surplus Before Ruin in the Generalized Erlang(n) Risk Model Perturbed by Diffusion

作　　者：王姗姗[1] 张春生[1] 

机构地区：[1]南开大学数学科学学院,天津300071

出　　处：《工程数学学报》2009年第5期786-796,共11页Chinese Journal of Engineering Mathematics

基　　金：The National Basic Research Program of China (973 Program) 2007CB814905;The Natural Science Foundation of China (10871102)

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。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. Particularly,we can deduce explicit results as long as the individual claim size is rationally distributed. Except for extending a number of results of simple generalized Erlang（n） risk model successfully, our arguments are more practical and the results are more delicate.

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-微分方程 

分 类 号：O211.6[理学—概率论与数理统计]