复合二项风险模型下Gerber-Shiu折现惩罚函数的渐近解

龚日朝;邹捷中

系统科学与数学 ›› 2007, Vol. 27 ›› Issue (4) : 573-586.

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中国科学院数学与系统科学研究院期刊网
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系统科学与数学 ›› 2007, Vol. 27 ›› Issue (4) : 573-586. DOI: 10.12341/jssms10250
论文

复合二项风险模型下Gerber-Shiu折现惩罚函数的渐近解

    龚日朝(1)(2), 邹捷中(2)
作者信息 +

An Asymptotic Relationship of the Gerber-Shiu Discount PenaltyFunction in the Compound Binomial Risk Model

    Gong Rizhao(1)(2), Zou Jiezhong(2)
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文章历史 +

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.

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.

关键词

复合二项风险模型 / Gerber-Shiu折现惩罚函数 / 渐近解 / 破产.

Key words

Compound binomial risk model / Gerber-Shiu discount penalty function / asympotic relationship / ruin.

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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. 系统科学与数学, 2007, 27(4): 573-586. https://doi.org/10.12341/jssms10250
Gong Rizhao , Zou Jiezhong. An Asymptotic Relationship of the Gerber-Shiu Discount PenaltyFunction in the Compound Binomial Risk Model. Journal of Systems Science and Mathematical Sciences, 2007, 27(4): 573-586 https://doi.org/10.12341/jssms10250
中图分类号： 62P05    62E20    60K30   
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