| 复合Poisson模型中“双界限”分红问题 |
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| 引用本文： | 高合理,尹传存. 复合Poisson模型中“双界限”分红问题[J]. 高校应用数学学报(A辑), 2008, 23(4) |
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| 作者姓名： | 高合理 尹传存 |
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| 作者单位： | 1. 滨州学院数学与信息科学系,山东,滨州,256603;曲阜师范大学数学科学学院,山东,曲阜,273165
2. 曲阜师范大学数学科学学院,山东,曲阜,273165 |
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| 基金项目： | 国家自然科学基金 ， 教育部科技重点项目 |
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| 摘 要： | 引入了复合Poisson模型中的"双界限"分红模型,在这种模型中,当盈余超过上限时分红以不超过保费率的速率付出,低于下限后保费率增大.文中利用Gerber- Shiu函数来分析这种模型,先导出了Gerber-Shiu函数m_1,m_2,m_3满足的积分-微分方程,再给出m_1,m_2,m_3的解析表示,最后通过几步把Gerber-Shiu函数m(u;b_1,b)的解析式表示出来.
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| 关 键 词： | 复合Poisson模型 threshold strategy模型 Gerber-Shiu函数 积分-微分方程 更新方程 |
Compound Poisson risk model with double-threshold dividend strategy |
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| GAO He-li,YIN Chuan-cun. Compound Poisson risk model with double-threshold dividend strategy[J]. Applied Mathematics A Journal of Chinese Universities, 2008, 23(4) |
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| Authors: | GAO He-li YIN Chuan-cun |
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| Abstract: | In this paper,the classical compound Poisson risk model with a double-threshold dividend strategy is considered.Under such a strategy,when the surplus is above the upper barrier, dividends are paid at a constant rate that does not exceed the premium rate,and the premium rate increases if the surplus falls below the lower barrier.Three integro-differential equations for the Gerber- Shiu discounted penalty function are derived,and analytical expressions for the Gerber-Shiu discounted penalty function m_1,m_2 and m_3 are obtained.Finally,the discounted penalty function m(u;b_1,b) may be expressed analytically in several steps. |
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| Keywords: | compound Poisson risk model threshold dividend strategy Gerber-Shiu discounted penalty function integro-differential equation renewal equation |
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