| 具有二步保费的Erlang（2）风险模型 |
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| 引用本文： | 孙景云,达高峰.具有二步保费的Erlang（2）风险模型[J].应用数学,2008,21(3). |
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| 作者姓名： | 孙景云 达高峰 |
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| 作者单位： | 兰州大学数学与统计学院,甘肃,兰州,730000 |
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| 摘 要： | 本文考虑了当索赔间隔时间为Erlang(2)分布且保费收取为二步保费过程的复合更新风险模型,推导出该模型的罚金折现期望值函数满足具有一定边界条件和积分微分方程,并解出该方程.特别地,当索赔额为指数分布时,利用所得结果给出了破产时间的Laplace变换及终积破产概率的解析解.
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| 关 键 词： | 复合更新过程 Erlang(2)分布 积分微分方程 罚金折现期望值函数 破产时刻 二步保费 Compound renewal process Erlang(2) distribution Integro-differential equation Gerber-Shiu dicounted penalty function Time of ruin two-step premium 保费 Erlang 风险模型 Rate Premium Model explicit result Laplace transform time of ruin ruin probability sizes equation boundary condition function derived distributed compound risk process premium |
The Erlang(2) Risk Model with a Two-step Premium Rate |
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| SUN Jing-yun,DA Gao-feng.The Erlang(2) Risk Model with a Two-step Premium Rate[J].Mathematica Applicata,2008,21(3). |
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| Authors: | SUN Jing-yun DA Gao-feng |
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| Abstract: | In this paper,we consider a compound renewal risk process with a two-step premium rate in which the claim waiting times are Erlang(2) distributed.An integro-differential equation with certain boundary condition for Gerber-Shiu function is derived and solved,and use this result we obtain the explicit result about the Laplace transform of the time of ruin and ruin probability when the claim sizes are exponentially distributed. |
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| Keywords: | Compound renewal process Erlang(2) distribution Integro-differential equation Gerber-Shiu dicounted penalty function Time of ruin two-step premium |
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