| 具有线性红利界限的破产理论 |
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| 引用本文： | 宗昭军,胡锋,元春梅.具有线性红利界限的破产理论[J].工程数学学报,2006,23(2):319-323. |
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| 作者姓名： | 宗昭军 胡锋 元春梅 |
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| 作者单位： | 1. 曲阜师范大学数学科学学院,山东,曲阜,273165
2. 江苏工业学院信息科学系,江苏,常州,213016 |
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| 基金项目： | 中国科学院资助项目;教育部科学技术研究项目;曲阜师范大学校科研和教改项目 |
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| 摘 要： | 本文讨论了存存线性红利界限的带随机干扰的经典风险模型,给出了破产概率的一个上界,并证明了生存概率及红利付款的期望现值分别满足一个积分-微分方程。最后给出了索赔额服从指数分布时生存概率及红利付款的期望现值的确切表达式。
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| 关 键 词： | 破产概率 线性红利界限 积分-微分方程 红利付款的期望现值 |
| 文章编号： | 1005-3085(2006)02-0319-05 |
| 收稿时间： | 2003-12-15 |
| 修稿时间： | 2003年12月15 |
The Ruin Theory in the Presence of a Linear Dividend Barrier |
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| ZONG Zhao-jun,HU Feng,YUAN Chun-mei.The Ruin Theory in the Presence of a Linear Dividend Barrier[J].Chinese Journal of Engineering Mathematics,2006,23(2):319-323. |
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| Authors: | ZONG Zhao-jun HU Feng YUAN Chun-mei |
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| Affiliation: | 1- Department of Mathematics, Qufu Normal University, Qufu 273165; 2. Department of Information Science, Jiangsu Polytechnic University, Changzhou 213016 |
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| Abstract: | This paper discusses the classical risk model perturbed by diffusion in the presence of a linear dividend barrier. An upper bound of ruin probability is given. Furthermore, we show that the survival probability and the expectation of the discounted dividend payments fulfill integro-differential equations, respectively. Finally, the explicit formulae for them are derived when the claim size is exponentially distributed. |
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| Keywords: | ruin probability linear dividend barrier integro-differential equation the expectation of the discounted dividend payments |
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