| 复合二项风险模型下Gerber-Shiu折现惩罚函数的渐近解 |
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| 引用本文： | 龚日朝,邹捷中. 复合二项风险模型下Gerber-Shiu折现惩罚函数的渐近解[J]. 系统科学与数学, 2007, 27(4): 573-586 |
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| 作者姓名： | 龚日朝 邹捷中 |
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| 作者单位： | 1. 湖南科技大学商学院,湘潭,411201;中南大学数学与计算技术学院,长沙,410075
2. 中南大学数学与计算技术学院,长沙,410075 |
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| 基金项目： | 国家自然科学基金;湖南省自然科学基金;湖南省社会科学基金;湖南省教育厅青年基金 |
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| 摘 要： | 首先研究了二项风险模型下Gerber-Shiu折现惩罚函数所满足的瑕疵更新方程,然后根据离散更新方程理论研究了其渐近解,并得到了破产概率、破产即刻前赢余和破产时刻赤字的联合分布分布以及其边际分布等的渐近解,进一步完善了Pavlova K P和Willmot G E 2004年发表的相关问题的结果.
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| 关 键 词： | 复合二项风险模型 Gerber-Shiu折现惩罚函数 渐近解 破产 |
| 收稿时间： | 2005-09-15 |
| 修稿时间： | 2005-09-15 |
An Asymptotic Relationship of the Gerber-Shiu Discount PenaltyFunction in the Compound Binomial Risk Model |
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| Gong Rizhao,Zou Jiezhong. An Asymptotic Relationship of the Gerber-Shiu Discount PenaltyFunction in the Compound Binomial Risk Model[J]. Journal of Systems Science and Mathematical Sciences, 2007, 27(4): 573-586 |
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| Authors: | Gong Rizhao Zou Jiezhong |
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| Affiliation: | (1)School of Business, Hunan Science and Technology University, Xiangtan 411201; (2)School of Mathematical Science and Computing Technology, Central South University, Changsha 410075 |
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| Abstract: | his paper considers the compound binomial risk model, studies the defective renewal equation satisfied by the Gerber-Shiu discount penalty function, and obtains the asymptotic relationship of the the Gerber-Shiu discount penalty function basied on the renewal theory. Furthermore, the asymptotic relationships of the joint distributions and the marginal distributions of the deficit at ruin and the surplus immediately prior to ruin are given.These results extend that obtained by Pavlova and Willmot in 2004. |
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| Keywords: | Compound binomial risk model Gerber-Shiu discount penalty function asympotic relationship ruin. |
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