History and Current Situation of Bankruptcy Theory Study

Abstract

Abstract: The researches of ruin theory carried out for nearly a century are reviewed generally.First,the clear descriptions,basic assumptions and main results of Lundberg-Cramer classical ruin model are given.Second,the main contributions of Hans GERBER,the leading scholar in ruin theory,and his group are analyzed on emphasis;and two modern approaches,renewal limit theorem and martingale,in researches of ruin theory are introduced.

Key words: ruin probability, adjustment coefficient, renewal theory, martingale

XU Shen-Xin, FANG Da-Fan. History and Current Situation of Bankruptcy Theory Study[J]. journal6, 2008, 29(1): 29-33.

References

[1] LUNDBERG F I.Approximerad Framstallning av Sannolikhetsfunktionen.II.Aterforsakring av Kollektivrisker [M].Almqvist Wiksell,Uppsala，1903.

[2] CRAMER H.On the Mathematical Theory of Risk [M].Stockholm:Shandia Jubilee,1930.

[3] CRAMER H.Mathematical Methods of Statistics [M].Princeton:Stockholm and Princeton Univ. Press. Almqvist Wiksell，1945.

[4] CRAMER H.On Some Questions Connected with Mathematical Risk [J].University of California Publ. Statistics，1954，2:99-123.

[5] CRAMER H.Collective Risk Theory [M].Stockholm:Skandia Jubilee Volume,1955.

[6] 严颖,成世学,程侃.运筹学随机模型 [M].北京:中国人民大学出版社，1995.

[7] CRAMER H.Half a Century with Probability Theory:Some Personal Recollection [J].Ann. Probab,1976,4:509-547.

[8] GERBER H U.成世学,严颖,译.数学风险论导引 [M].北京:世界图书出版发行公司，1997.

[9] GRANDELL J.Aspects of Risk Theory [M].New York:Springer Verlag，1991.

[10] FELLER W.An Introduction to Probability Theory and Its Application [M].New York:John Wiley Sons,1971.

[11] DUFRESNE F,GERBER H U,SHIU E S W.Risk Theory with the Gamma Process [J].ASTIN Bulletin,1991,21:177-192.

[12] DUFRESNE F，GERBER H U.The Probability of Ruin for the Inverse Gaussian and Related Processes [J].Insurance:Mathematics and Economics，1993，12:9-22.

[13] DUFRESNE F，GERBER H U.Risk Theory for the Compound Poisson Processes that is Perturbed by Diffusion [J].Insurance:Mathematics and Economics，1991，10:51-59.

[14] GERBER H U，GOOVAERTS M J，KASS R.On the Probability and Severity of Ruin [J].ASTIN Bulletin，1987，17:151-183.

[15] DUFRESNE F，GERBER H U.The Surpluses Immediately before and at Ruin,and the Amount of the Claim Causing Ruin [J].Insurance:Mathematics and Economics，1988，7:193-199.

[16] GERBER H U.Mathematical Fun with the Compound Binomial Process [J].ASTIN Bulletin，1988，18:161-168.

[17] EMBRECHTS P，VERAVERBEKE N.Estimates for the Probability of Ruin with Special Emphasis on the Possibility of Large Claims [J].Insurance:Mathematics and Economics，1982，1:55-72.

[18] EMBRECHTS P，KLUPPELBERG C，MIKOSCH T.Modelling Extremal Events for Insurance and Finance [M].New York:Springer-Verlag,1997.

[19] GOLDIE C M，KLUPPELBERG C.Subexponential Distributions [M]//ADLER R.A Practical Guide to Heavy Tails. Birkhauser,1988：435-459.

[20] 唐启鹤.重尾索赔下关于破产概率的一个等价式 [J].中国科学(A辑)，2002，32(3):260-266.

[21] 孔繁超,曹龙.更新风险模型和延迟更新风险模型中破产概率的若干结果 [J].数学年刊,2003，24A:1,119-128.

[22] 江涛,陈宜清.平稳更新模型下生存概率的一个局部等价式 [J].中国科学(A辑),2004，34(4):385-391.

[23] WANG Han-xing,FANG Da-fan,TANG Mao-ning.Ruin Probabilities Under a Markovian Risk Model [J].Acta. Math. Appl. Sinica,2003，19(4)：621-630.

[24] 龚日朝,邹捷中.重尾索赔下更新风险模型生存概率局部估计解 [J].应用数学学报，2006，29(5)：947-954.

[25] 王超,周斌,程东亚,等.带随机重延迟的大额索赔更新风险模型的局部破产概率 [J].应用概率统计,2006，22(1)：63-68.