带干扰的广义Erlang(n)风险模型破产前首次达到给定水平的时间(英文)  

The First Time of Reaching the Given Level before Ruin in the Generalized Erlang(n) Risk Model Perturbed by Diffusion

作　　者：孙国红[1] 张春生[2] 

机构地区：[1]天津农学院基础科学系,天津300384 [2]南开大学数学科学学院,天津300071

出　　处：《南开大学学报（自然科学版）》2010年第4期106-112,共7页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported by the Natural Science Foundation of Tianjin(08JCYBJC02200);the Natural Science Foundation of China(10871102);National Basic Research Program of China(973 Program) (2007CB814905)

摘　　要：主要讨论了带干扰的广义Erlang(n)风险模型破产前首次达到给定水平的时间的拉普拉斯变换.推导并解出这一拉普拉斯变换所满足的具有一定边界条件的积分-微分方程,当索赔服从指数分布时,给出了显式解.The generalized Erlang（n） risk model perturbed by diffusion is considered and the Laplace transform of the first time to attain the specified level prior to ruin is discussed mainly. A homogeneous integro-differential equation for this Laplace transform is derived and solved with certain boundary conditions. Finally, explicit expressions are given when the individual claim sizes are rationally distributed.

关 键 词：SPARRE ANDERSEN风险模型 广义Erlang(n)索赔间隔 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]