| 带扰动的广义Erlang(n)风险过程最大亏损问题研究 |
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| 引用本文： | 王健,王传玉,周金乐. 带扰动的广义Erlang(n)风险过程最大亏损问题研究[J]. 盐城工学院学报(自然科学版), 2015, 28(1): 9-15 |
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| 作者姓名： | 王健 王传玉 周金乐 |
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| 作者单位： | 安徽工程大学数理学院,安徽芜湖,241000;安徽工程大学数理学院,安徽芜湖,241000;安徽工程大学数理学院,安徽芜湖,241000 |
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| 基金项目： | 国家自然科学基金项目(61203139);安徽省重点教研项目(2012jyxm277) |
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| 摘 要： | 运用Laplace变换,研究了带扰动的广义Erlang(n)风险模型最大亏损的分布,求得满足生存概率的一个积分-微分方程的解。它的解可以表示为2n阶线性独立特解的一个线性组合,当n=2时,得到最大亏损分布的精确表达式,再通过一个实例来说明该研究结果。
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| 关 键 词： | 带扰动的广义Erlang(n)风险模型 广义Erlang(n)索赔间隔 积分-微分方程 最大亏损 |
The Maximum Severity of Ruin in a Generalized Erlang(n) Risk Process Perturbed by Diffusion |
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| WANG Jian,WANG Chuanyu and ZHOU Jinle. The Maximum Severity of Ruin in a Generalized Erlang(n) Risk Process Perturbed by Diffusion[J]. Journal of Yancheng Institute of Technology(Natural Science Edition), 2015, 28(1): 9-15 |
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| Authors: | WANG Jian WANG Chuanyu ZHOU Jinle |
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| Affiliation: | WANG Jian;WANG Chuanyu;ZHOU Jinle;School of Mathematics and Physics,Anhui Polytechnic University; |
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| Abstract: | In this paper , we discuss the distribution of the maximum severity of ruin from the time of ruin until the time that the surplus returns to level 0 in a generalized Erlang(n) risk process perturbed by diffusion.Then, we solve an integro-differential equation that is satisfied by the survival probability by the way of Laplace transform .Its solution can be expressed as a linear combination of 2n linearly independent particular solutions of the integro -differential equation .When n=2, the maximum sever-ity of ruin can be expressed explicitly in terms of the non -ruin probability.Finally, the research results of this paper are illustra-ted through an instance . |
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| Keywords: | the generalized Erlang ( n) risk process perturbed by diffusion generalized Erlang (n) claim waiting time the integro-differential equation the maximum severity of ruin |
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