[1]张 敏,张志民.马氏调节风险模型下的破产前盈余分布[J].江西师范大学学报(自然科学版),2016,40(06):608-612.
 ZHANG Min,ZHANG Zhimin.On the Distribution of the Surplus Before Ruin in a Markov-Modulated Risk Model[J].,2016,40(06):608-612.
点击复制

马氏调节风险模型下的破产前盈余分布()
分享到:

《江西师范大学学报》(自然科学版)[ISSN:1006-6977/CN:61-1281/TN]

卷:
40
期数:
2016年06期
页码:
608-612
栏目:
出版日期:
2016-12-01

文章信息/Info

Title:
On the Distribution of the Surplus Before Ruin in a Markov-Modulated Risk Model
作者:
张 敏张志民
1.眉山职业技术学院,四川 眉山 620000; 2.重庆大学数学与统计学院,重庆 401331
Author(s):
ZHANG MinZHANG Zhimin
1.Meishan Vocational and Technical College,Meishan Sichuan 620000; 2.College of Mathematics and Statistics,Chongqing University,Chongqing 401331
关键词:
马氏调节风险模型 破产时刻 破产前盈余 破产时赤字 Dickson公式
Keywords:
Markov-modulated risk model time of ruin surplus before ruin deficit at ruin dickson’s formula
分类号:
O 211.6
摘要:
对在马氏调节风险过程中破产前盈余和破产时赤字的联合分布进行研究.该过程中的泊松索赔到达速率和索赔额分布随时间改变,并取决于1个潜在的马尔科夫跳过程的状态.推广了Dickson公式,并证明了破产前盈余的分布函数和密度函数均能由破产概率表示出来.
Abstract:
The joint distribution of the surplus before ruin and the deficit at ruin in a Markov-modulated risk process in which the rate for the Poisson claim arrivals and the distribution of the claim sizes vary in time depending on the state of an underlying(external)Markov jump process is studied.The Dickson’s formula from the classical risk model to the Markov-modulated risk model is extended and it is shown that both of the distribution function and density function of the surplus before ruin can be expressed in terms of the ruin probabilities.

参考文献/References:

[1] Asmussen S.Risk theory in a Markovian environment [J].Scandinavian Actuarial Journal,1989(2):69-100.
[2] Zhu Jinxia Yang Hailiang.Ruin theory for a Markov regime-switching model under a threshold dividend strategy [J].Insurance:Mathematics and Economics,2008,42(1):311-318.
[3] Li Jingchao,D C M,Li Shuanming.Some ruin problems for the MAP risk model [J].Insurance:Mathematics and Econmics,2015,65:1-8.
[4] Li Jingchao,Dickson D C M,Li Shuanming.Analysis of some ruin-related guantities in a Markov-modulated risk model [J].Stochastic Models,2016,32(3):351-365.
[5] Landriault D,Shi Tianxiang.Occupation times in the MAP risk model [J].Insurance:Mathematics and Economics,2015,60:75-82.
[6] Zhang Zhimin,Cheung E C K.The Markov additive risk process under an erlangized dividend barrier strategy [J].Methodology and Computing in Applied Probability,2016,18(2):275-306.
[7] Reinhard J M.On a class of semi-Markov risk models obtained as classical risk models in a Markovian environment [J].Astin Bulletin,1984,14(1):23-43.
[8] Asmussen S,Frey A,Rolski T,et al.Does Markovmodulation increase the risk? [J].Astin Bulletin,1995,25(1):49-66.
[9] Bauerle N.Some results about the expected ruin time in Markov modulated risk models [J].Insurance:Mathematics and Economics,1996,18(2):119-127.
[10] Schmidli H.Estimation of the Lundberg coefficient for a Markov modulated risk model [J].Scandinavian Actuarial Journal,1997(1):48-57.
[11] Wu Yanhong.Bounds for the ruin probability under a Markovian modulated risk model [J].Communications in Statistics.Stochastic Models,1999,15(1):125-136.
[12] Snoussi M.The severity of ruin in Markov-modulated risk models [J].Bulletin of the Swiss Association of Actuaries,2002(1):31-43.
[13] Lu Yi,Li Shuanming.On the probability of ruin in a Markov-modulated risk model [J].Insurance:Mathematics and Economics,2005,37(3):522-532.
[14] Lu Yi.On the severity of ruin in a Markov-modulated risk model [J].Scandinavian Actuarial Journal,2006(4):183-202.
[15] Li Shuanming,Lu Yi.Moments of the dividend payments and related problems in a Markov-modulated risk model [J].North American Actuarial Journal,2007,11(2):65-76.
[16] Ng A C Y,Yang Hailiang.Lundeberg-type bounds for the joint distribution of surplus immediately before and at ruin under a Markov-modulated risk model [J].Astin Bulletin,2005,35(2):351-361.
[17] Ng A C Y,Yang Hailiang.On the joint distribution of surplus before and after ruin under a Markovian regime switching model [J].Stochastic Processes and their Applications,2006,116(2):244-266.
[18] Li Shuanming,Lu Yi.The decompositions of the discounted penalty functions and dividend-penalty identity in a Markov-modulated risk model [J].Astin Bulletin,2008,38(1):53-71.
[19] Dickson D C M.On the distribution of the surplus prior to ruin [J].Insurance:Mathematics and Economics,1992,11(3):191-207.

备注/Memo

备注/Memo:
收稿日期:2016-09-20基金项目:国家自然科学基金(11471058,11101451)和重庆市自然科学基金(CSTC2014JCYJA00007)资助项目.通信作者:张志民(1981-),男,河北石家庄人,副教授,博士,博士生导师,主要从事精算数学和风险模型的研究.
更新日期/Last Update: 1900-01-01