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| 带扰动的广义 Erlang（n）风险过程最大亏损问题研究 |
| The Maximum Severity of Ruin in a Generalized Erlang(n) Risk Process Perturbed by Diffusion |
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| DOI： |
| 中文关键词: 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 |
| 英文关键词: 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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| 中文摘要: |
| 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。 |
| 英文摘要: |
| 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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