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数学进展
研究论文
破产论研究综述
The Survey for Researches of Ruin Theory

成世学
Cheng Shixue

中国人民大学信息学院 北京,100872,中国
(Information School, Renmin University of China, Beijing, 100872, P. R. China

收稿日期: 2002-10-25
出版日期: 2002-10-25

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摘要 本文在保险数学(亦称为精算数学)的范畴内,对破产论近百年的研究进展作了综述性的回顾.首先,给出了Lundbeg-Cramér经典破产模型的确切表述、基本假定和主要结论,并以当代研究破产论的两种主要途径:Feller的更新论证和 Gerber的鞅方法给出了这一模型主要结论的严格证明.其次,重点阐述了当代研究破产论的权威学者 Gerber及其合作者的主要研究成果,并更为简明地介绍了当代破产论研究中其他的主要进展和理论研究热点.最后,以精算学术界泰斗HansBühlmann关于第三类精算师的评述作为全文的总结.
关键词 破产概率破产时赤字破产前瞬时盈余调节系数更新论证鞅方法    
Abstract:In the context of Insurance Mathematics (also to be called Actuarial Mathema tics), the researches of ruin theory carried out nearly for century are reviewed generally. First, the clear descriptions, basic assumptions and main results of Lundberg-Cramer classical ruin model are given; Two modern approaches in researches of ruin theory are introduced and used to prove the conclusions of classical risk model concisely. Next, the main contributions of Professor Hans Gerber, the leading scholar in ruin theory, and his group are analysed on emphasis; The other advances in modern ruin theory are also briefly mentioned. Finally, the comments for the third kind of actuaries made by Professor Hans Bühlmann, the authoritative scholar in actuarial society, are used to summarize this paper.
Key words deficit of ruin    surplus immediately before ruin    adjustment coefficient    renewal argument    martingale approach
[1] 何敬民, 吴荣, 崔家峰. 保费依赖向后重现时间过程风险模型的破产概率上界 (英)[J]. 数学进展, 2011, 40(4): 501-511.
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