| 一类Sparre Andersen风险模型的Gerber-Shiu函数 |
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| 引用本文： | 范庆祝,尹传存. 一类Sparre Andersen风险模型的Gerber-Shiu函数[J]. 应用概率统计, 2009, 25(5): 499-512 |
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| 作者姓名： | 范庆祝 尹传存 |
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| 作者单位： | 1. 石河子大学商学院统计与金融系,五家渠,831300;曲阜师范大学数学科学学院,曲阜,273165
2. 曲阜师范大学数学科学学院,曲阜,273165 |
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| 基金项目： | 国家自然科学基金项目，山东省自然科学基金项目，教育部科技重点项目 |
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| 摘 要： | 本文考虑了一类相邻两次索赔的时间间隔服从Erlang($n$)和Erlang($m$)的混合分布的Sparre Andersen风险模型.主要目的是研究Gerber-Shiu函数$phi_delta(u)$,首先证明了$phi_delta(u)$满足一个高阶的积分微分方程,然后讨论了广义Lundberg方程根的性质,在此基础上导出了$phi_delta(u)$的拉普拉斯变换并且证明了$phi_delta(u)$满足一个更新方程,最后给出了一个例子.
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| 关 键 词： | Sparre Andersen风险模型 Erlang($n$) Gerber-Shiu函数 破产概率. |
The Gerber-Shiu Function for a Sparre AndersenRisk Model |
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| FAN QINGZHU,YIN CHUANCUN. The Gerber-Shiu Function for a Sparre AndersenRisk Model[J]. Chinese Journal of Applied Probability and Statisties, 2009, 25(5): 499-512 |
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| Authors: | FAN QINGZHU YIN CHUANCUN |
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| Affiliation: | Department of Statistics and Finance, School of Business, Shihezi UniversitySchool of Mathematical Sciences, Qufu Normal University |
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| Abstract: | In this paper, we consider a Sparre Andersen risk model in whichthe claim inter-arrival distribution is a mixture of an Erlang($n$)distribution and an Erlang($m$) distribution. Our purpose is tostudy the Gerber-Shiu function $phi_delta(u)$. First, we show that$phi_delta(u)$ satisfies a higher-order integro-differentialequation, and then we discuss the roots of the generalizedLundberg's equation. On this basis, we drive the Laplace transformof $phi_delta(u)$ and prove that $phi_delta(u)$ satisfies arenewal equation. Finally, we consider an example. |
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| Keywords: | Erlang(n) Sparre Andersen risk model Erlang(n) Gerber-Shin function ruin probability |
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