## 留言板

 引用本文: 王汉兴, 颜云志, 赵飞, 方大凡. 马氏风险过程[J]. 应用数学和力学, 2007, 28(7): 853-860.
WANG Han-xing, YAN Yun-zhi, ZHAO Fei, FANG Da-fan. Markovian Risk Process[J]. Applied Mathematics and Mechanics, 2007, 28(7): 853-860.
 Citation: WANG Han-xing, YAN Yun-zhi, ZHAO Fei, FANG Da-fan. Markovian Risk Process[J]. Applied Mathematics and Mechanics, 2007, 28(7): 853-860.

• 中图分类号: O211

## Markovian Risk Process

• 摘要: 研究了一般马氏风险过程，它是经典风险过程的拓广．具有大额索赔的风险过程用此马氏风险模型来描述是适合的．在此模型中,索赔到达过程由一点过程来描述,该点过程是一马氏跳过程从0到t时间段内的跳跃次数．主要研究了此风险模型的破产概率,得到了破产概率满足的积分方程,并应用本文引入的广更新方法,得到了破产概率的收敛速度上界．
•  [1] Grandell J.Aspects of Risk Theory[M].New York: Springer-Verlag,1991. [2] Gerber H U.An Introduction to Mathematical Risk Theory[M].S S Heubner Foundation Monograph series 8, Philadelphia,1979. [3] Mikosch T.Heavy-tailed modelling in insurance[J].Stochastic Models,1997,13(4)：799-816. [4] Klüppelbery C,Mikosch T.Large deviations of heavy-tailed random sums with applications in insurance and finance[J].J Appl Prob,1997,34(2):293-308. doi: 10.2307/3215371 [5] WANG Hang-xing,FANG Da-fan,TANG Mao-ning.Ruin probabilities under a markovian risk model[J].Acta Mathematicae Applicatae Sinica, English Series,2003,19(4)：621-630. [6] Asmussen S.Applied Probability and Queues[M].New York:John Wiley & Sons, 1987. [7] Asmussen S. Risk theory in a Markovian environment[J].Scand Act J,1989,69-100. [8] Wang Y H.Bounds for the ruin probability under a Markovian modulated risk model[J].Stochastic Models,1999,15(1)：125-136. [9] Blaszczyszyn B,Rolski T.Expansions for Markov-modulated systems and approximations of ruin probability[J].J Appl Prob,1996,33:57-70. doi: 10.2307/3215264

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##### 出版历程
• 收稿日期:  2006-11-07
• 修回日期:  2007-04-26
• 刊出日期:  2007-07-15

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