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| 保费随机的离散风险模型的罚金期望函数 | |
| 引用本文： | 方世祖,赵培臣,张春梅.保费随机的离散风险模型的罚金期望函数[J].应用数学,2008,21(4). |
| 作者姓名： | 方世祖 赵培臣 张春梅 |
| 作者单位： | 1. 西安交通大学理学院,陕西,西安,710049;广西大学数学与信息科学学院,广西,南宁,530004 2. 菏泽学院数学系,山东,菏泽,274015 3. 广西大学数学与信息科学学院,广西,南宁,530004 |
| 基金项目： | 广西大学校科研和教改项目 |
| 摘 要： | 本文把经典的复合二项风险模型进行推广,其中保费收取方式不再是时间的线性函数而是一个二项过程.我们把它的罚金期望看成初始资本的函数,得到了罚金期望函数的递推公式和渐近估计,最后利用罚金期望函数的递推公式和渐近估计给出了几个重要的破产量的递推公式及其渐近估计. |
| 关 键 词： | 罚金期望函数 复合二项过程 递推公式 离散更新方程 渐近估计 |
The Expected Discounted Penalty Function at Ruin of the Discrete Risk Model with Random Income |
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| FANG Shi-zu,ZHAO Pei-chen,ZHANG Chun-mei.The Expected Discounted Penalty Function at Ruin of the Discrete Risk Model with Random Income[J].Mathematica Applicata,2008,21(4). | |
| Authors: | FANG Shi-zu ZHAO Pei-chen ZHANG Chun-mei |
| Abstract: | In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function.We examine the expected discounted value of a penalty at ruin,which is considered as a function of the initial surplus.A mathematically recursive formula is derived for the expected discounted penalty function,the asymptotic estimate for the expected discounted penalty function is then given.Finally, we give some examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function. |
| Keywords: | Discounted penalty function Compound binomial process Reeursive for-mula Discrete renewal equation Asymptotic estimate |
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