广义Erlang(2)风险模型下破产时和破产前索赔次数的联合密度(英文)  

Joint Density of the Number of Claims until Ruin and the Time to Ruin in the Generalized Erlang(2) Risk Model

作　　者：李彦红[1] 赵春明[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：《南开大学学报（自然科学版）》2015年第1期92-102,共11页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported by National Natural Science Foundation of China(11171164,11271385,11371020)

摘　　要：研究了广义Erlang(2)风险模型,利用Lagrange展开定理得出了初值为零时破产时和破产前索赔次数的联合密度表达式,并利用概率论证的方法进一步得出了初值大于零时破产时和破产前索赔次数的联合密度.最后,用两个例子来说明前面的结论.A geeralized Erlang（2）risk model is considered,where the individual claim amount can be an arbitrary positive random variable.First,by employing the Lagrange＇s expansion theorem,a closed-form expression for the joint density of the number of claims until ruin and the time to ruin is derived when the initial surplus is zero.Second,applying probabilistic arguments,a formula for the joint density of the number of claims until ruin and the time to ruin is obtained when the initial surplus is greater than zero.Finally,examples with exponential and mixture Erlang distributed claims are given,respectively,to illustrate the results.

关 键 词：广义Elrlang(2)风险模型 联合密度 破产时 破产前索赔次数 

分 类 号：O211.6[理学—概率论与数理统计]