阈值分红策略下具有PH索赔分布的风险过程的破产时间分析
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摘要
本文分析阈值分红策略下具有PH索赔分布的风险过程,并给出计算这一风险模型的新破产时间的方法.将阈值分红策略下的风险过程转化为有限容量的Markov流体队列(FMFQ)模型,在FMFQ模型中,引入一个新的连续积累过程用以刻画FMFQ中系统在特定状态中的停留时间,从而得到风险过程的破产时间.应用FMFQ理论及转换关系,得到阈值分红策略下具有PH索赔分布的风险过程破产时间的Laplace-Stieltjes变换(LST)表示式,并给出风险过程的最终破产概率的解析表示式.
In this paper,we analyzed a risk model with phase-type claims under a threshold dividend strategy,and proposed a novel algorithm to obtain the Laplace-Stieltjes transform( LST) of the ruin time. We first transformed this risk process into a Finite Markov Fluid Queue( FMFQ),and then proposed a new continuous accumulative process,from which the ruin time of the risk model can be obtained. Using the FMFQ theory,we obtained the LST expressions of the ruin time,and also derived the analytical expression for the ultimate ruin probability.
In this paper,we analyzed a risk model with phase-type claims under a threshold dividend strategy,and proposed a novel algorithm to obtain the Laplace-Stieltjes transform( LST) of the ruin time. We first transformed this risk process into a Finite Markov Fluid Queue( FMFQ),and then proposed a new continuous accumulative process,from which the ruin time of the risk model can be obtained. Using the FMFQ theory,we obtained the LST expressions of the ruin time,and also derived the analytical expression for the ultimate ruin probability.
引文
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[14]张超权,刘晓辉.求解MArP风险过程破产时间的新方法[J].统计与决策,2015(21):20-23.
[15] AHN S,RAMASWAMI V. Efficient algorithms for transient analysis of stochastic fluid flow models[J]. J Appl Prob,2005,42(2):531-549.
[16] BEAN N,TAYLOR P. Hitting probabilities and hitting times for stochastic fluid flows:the bounded model[J]. Prob Eng Inform Sci,2009,23(1):121-147.
[17] ABATE J,WHITT W. Numerical inversion of Laplace transforms of probability distributions[J]. ORSA J Comput,1995,7(1):36-43.
[2] ALBRECHER H,GERBER H U,SHIU E S W. The optimal dividend barrier in the Gamma-Omega model[J]. Eur Actuar J,2011,1(1):43-55.
[3]王爽.基于多目标规划的保险公司资产负债管理定量方法的研究[D].重庆:重庆工商大学,2012.
[4] AVANZI B,GERBER H U,SHIU E S W. Optimal dividends in the dual model[J]. Insur Math Econ,2007,41(1):111-123.
[5] NG A C Y. On a dual model with a dividend threshold[J]. Insur Math Econ,2009,44(2):315-324.
[6]何庆国,何传江.阈值分红策略下带常利率的对偶风险模型[J].经济数学,2012,29(4):67-70.
[7] RAMASWAMI V. Matrix analytic methods for stochastic fluid flows[C]. Proceedings of the 16th International Teletraffic Congress,Edinburgh,7-11 June 1999; 1019-1030.
[8] BEAN N G,OREILLY M M,TAYLOR P G. Algorithms for the Laplace-Stieltjes transforms of first return probabilities for stochastic fluid flows[J]. Meth Compu Appl Prob,2008,10(3):381-408.
[9] ASMUSSEN S. Stationary distributions via first passage times[J]. In Advances in Queueing:Theory,Methods,and Open Problems,ed. J. Dshalalow,CRC Press,Boca Raton,FL,1995,79-102.
[10] BADESCU A L,BREUER L,SOARES A D,et al. Risk processes analyzed as fluid queues[J]. Scand Actuar J,2005,15(1):127-141.
[11] BADESCU A L,DAVID L. Applications of fluid flow matrix analytic methods in ruin theory-a review[J]. Rev R Acad Cerie A Mat,2009,103(2):353-372.
[12] RAMASWAMI V. Passage times in fluid models with application to risk processes[J]. Meth Comput Appl Prob,2006,8(4):497-515.
[13] NIGEL G,BEAN. A stochastic two-dimensional fluid model[J]. Stoch Models,2013,29(1):31-63.
[14]张超权,刘晓辉.求解MArP风险过程破产时间的新方法[J].统计与决策,2015(21):20-23.
[15] AHN S,RAMASWAMI V. Efficient algorithms for transient analysis of stochastic fluid flow models[J]. J Appl Prob,2005,42(2):531-549.
[16] BEAN N,TAYLOR P. Hitting probabilities and hitting times for stochastic fluid flows:the bounded model[J]. Prob Eng Inform Sci,2009,23(1):121-147.
[17] ABATE J,WHITT W. Numerical inversion of Laplace transforms of probability distributions[J]. ORSA J Comput,1995,7(1):36-43.