| Sparre Andersen风险模型破产时刻和破产赤字的联合密度函数 |
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| 引用本文： | 徐怀,唐玲.Sparre Andersen风险模型破产时刻和破产赤字的联合密度函数[J].浙江大学学报(理学版),2013,40(4):401-405. |
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| 作者姓名： | 徐怀 唐玲 |
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| 作者单位： | 1. 安徽大学数学科学学院,安徽合肥,230039
2. 安徽建筑工业学院数理系,安徽合肥,230601 |
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| 摘 要： | 假设索赔额服从指数分布时，在普通更新风险模型中，应用Kendall等式，给出破产时刻的密度函数.然后使用概率方法得到普通更新风险模型和延迟更新风险模型中破产时刻和破产赤字的联合密度函数的解析表达式.最后考虑了当索赔间隔时间为Erlang(2)分布的数值例子，并绘图给予了说明.
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| 关 键 词： | Kendall等式 破产时刻 破产赤字 Erlang(2)分布 联合密度函数 |
| 收稿时间： | 2011-06-13 |
The joint density of the time to ruin and the deficit at ruin for a Sparre Andersen risk model |
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| XU Huai
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TANG Ling.The joint density of the time to ruin and the deficit at ruin for a Sparre Andersen risk model[J].Journal of Zhejiang University(Sciences Edition),2013,40(4):401-405. |
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| Authors: | XU Huai TANG Ling |
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| Institution: | 1. School of Mathematics, Anhui University, He f ei 230039, China; 2. Department of Mathematics, Anhui Institute of Architecture and Industry, He f ei 230601, China) |
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| Abstract: | The ordinary renewal risk model and derive expressions for the density of the time to ruin are considered when the individual claim amount distribution is an exponential distribution. The derivation is based on Kendall＇s identity. Then by using probabilistic argument, an expression for joint density of the time to ruin and the deficit at ruin for the delayed renewal risk model and the ordinary renewal risk model are obtained. Finally the results in the cases of Erlang（2） inter-claim time are illustrated. |
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| Keywords: | Kendall's identity the time to ruin the deficit at ruin Erlang(2) distribution joint density function |
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