Erlang风险模型有限时间的破产概率

中国管理科学 ›› 2006, Vol. ›› Issue (1): 112-116.

Erlang风险模型有限时间的破产概率

江涛

南京财经大学金融学院, 江苏, 南京, 210003

收稿日期:2005-05-08 修回日期:2005-12-08 出版日期:2006-02-28 发布日期:2012-03-07
基金资助:
国家自然科学基金项目(70471071);江苏省哲社基金项目(04SJB630005);江苏省青蓝工程学术带头人基金项目资助

Finite Time Ruin Probability in Erlangian Risk Model with Constant Interest Force

JIANG Tao

School of Finance, Nanjing University of Finance and Economics, Nanjing 210003, China

Received:2005-05-08 Revised:2005-12-08 Online:2006-02-28 Published:2012-03-07

摘要/Abstract

摘要： Erlang风险模型广泛应用于排队论、控制论以及金融风险过程.本文在索赔来到(claim-arrival)为Erlang过程,索赔额服从帕雷托分布以及具有常数利息力度的假设下,得到了有限时间内破产概率的渐近表达公式.该结果实质性地推广了Kluppelberg and Stadtmuller[1]和Tang[2]的结果:前者考虑了无穷时间的破产概率,而后者考虑的过程局限为泊松的.由破产模型与排队模型之间的联系可知,本文的结果在管理科学中有许多应用.

关键词: Erlang风险模型, 有限时间破产概率, 常数利息力度, 帕雷托分布

Abstract: Erlangian risk model is widely used in queueing theory,control theory and finance risk models.Under the assumptions that the claim-arrival follows Erlangian process,the claim-size is Paretian distributed and the constant interest force exists,this paper obtains the asymptotic formula of finite-time ruin probability,that essentially extends the corresponding results of reference^[1] which only deals with ultimate time ruin probability,and reference^[2] which merely limits the model to the Poisson case.By the relationship between ruin model and queueing model we know that the results we obtain can be applied to management science in many aspects.

Key words: Erlangian risk model, finite time ruin probabilities, constant interest force, Pareto-type claim-size

中图分类号:

O211.1

江涛. Erlang风险模型有限时间的破产概率[J]. 中国管理科学, 2006, (1): 112-116.

JIANG Tao. Finite Time Ruin Probability in Erlangian Risk Model with Constant Interest Force[J]. Chinese Journal of Management Science, 2006, (1): 112-116.

参考文献

[1] Kluppelberg and Stadtmuller,U..Ruin probabilities in the presence of heavy-tails and interest rates[J].Scand Actuar J.,1998,(1):49-58.
[2] Tang,Q..The finite time ruin probability of the compound Poisson model with constant interest force[J].J.Appl.Probab.,2005,42(3):608-619.
[3] 江涛.GI/G/l/∞排队系统平稳等待时间的渐进等价公式[J].数学物理学报,2004,(6):752-757.
[4] Ross,S.Stochastic Processes[M].Wiley,New York,1983.
[5] Asmussen S..Applied Probability and Queues[M].Chichester,John Wiley Sons,Ltd.,Chichester,1987.
[6] 常玉林,王炜等.双车道公路车头时距分布模型研究及应用[J].东南大学学报,1999,29(6).
[7] Kalashnikov V.and Konstantinides D..Ruin under interest force and subexponential claims:a simpletreatment[J].Insurance Math.Econom.,2000,35:513-525.
[8] Konstantinides,D.,Tang Q.and Tsitsiashvili,G.Sh..Estimates for the ruin probability in the classical risk model with constant interest force in the presence of heavy tails[J].Insurance Math.Econom.,2002,31 (3):447-460.
[9] Cai,J.and Dickson D..Ruin probabilities with a Markov chain interest model[J].Insurance Math.Econom.,2004,35:513-525.
[10] 尹传存,关于破产概率的一个局部定理[J].中国科学,2004,34(2):192-202.
[11] Resnick,S.I.and Willekens,E..Moving averages with random coefficients and random coefficient autoregressive models[J].Comm Statist Stochastic Models,1991,7 (4):511-525.
[12] Embrechts,P.,Kluppelberg,C.and Miko sch,T..Modelling Extremal Events for Insurance and Finance[M].Springer-Verlag,Berlin,1997.
[13] Rolski T.,Schmidli H.,Schmidt V.et al.J.Stochastic Processes for Insurance and Finance[M].John Wiley Sons,Ltd.,Chichester,1999.
[14] 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,2004,34(4):385-391.
[15] 毛泽春,刘锦萼.免赔额和NCD赔付条件下保险索赔次数的分布[J].中国管理科学,2005,13(5):1-5.
[16] Maria De Lourdes and Centeno.Excess of Loss Reinsurance and The Probability in Finite Horizon[J].ASTIN,1997,27(1),59-70.