随机环境下具有阈值分红策略的风险过程的破产时间分析
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摘要
本文提出随机环境下的阈值分红策略下PH索赔分布的风险过程,给出这一风险模型的破产时间Laplace-stieltjes变换(LST)解析式的一种新的求解方法。即,忽略风险过程的初始盈余,将其转化为相应的初始水平为0的有限的Markov流体队列(FMFQ)模型,应用FMFQ理论,根据风险过程的破产时间与对应FMFQ忙期的关系,得到风险过程破产时间的LST表示式,同时也推得最终破产概率的解析表示式。
In this paper,a threshold dividend strategy risk model with phase-type claims under stochastic environment is analyzed and a novel algorithm to obtain the Laplace-stieltjes transform(LST)of the ruin time is proposed.The initial surplus of the risk process is neglected,and the risk process is transformed into a Finite Markov Fluid Queue(FMFQ)with initial level zero.Using the FMFQ theory,the LST expressions of the ruin time are obtained through the relationship between the ruin time of the risk process and the busy period of the FMFQ,and the expression of ultimate ruin probability is also presented.
In this paper,a threshold dividend strategy risk model with phase-type claims under stochastic environment is analyzed and a novel algorithm to obtain the Laplace-stieltjes transform(LST)of the ruin time is proposed.The initial surplus of the risk process is neglected,and the risk process is transformed into a Finite Markov Fluid Queue(FMFQ)with initial level zero.Using the FMFQ theory,the LST expressions of the ruin time are obtained through the relationship between the ruin time of the risk process and the busy period of the FMFQ,and the expression of ultimate ruin probability is also presented.
引文
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[14]BEAN N G,O’REILLY M M,TAYLOR P G.Hitting probabilities and hitting times for stochastic fluid flows:the bounded model[J].Probability in the Engineering and Informational Sciences,2009,23(1):121-147.DOI:10.1017/S0269964809000102.
[15]ABATE J,WHITT W.Numerical inversion of Laplace transforms of probability distributions[J].ORSA Journal on Computing,1995,7(1):36-43.DOI:10.1287/ijoc.7.1.36.
[2]杨龙.多层分红策略下以FGM Copula为相依结构的风险模型[J].数学物理学报,2015,35A(5):1004-1017.DOI:10.3969/j.issn.1003-3998.2015.05.016.
[3]岳毅蒙.最小盈余约束下风险模型的最优分红策略[J].甘肃科学学报,2015,27(2):19-24.DOI:10.16468/j.cnki.issn1004-0366.2015.02.005.
[4]温玉卓,唐胜达,邓国和.随机环境下相关多险种风险过程破产时间的Asmussen算法[J].广西师范大学学报(自然科学版),2016,34(3):68-73.DOI:10.16088/j.issn.1001-6600.2016.03.010.
[5]唐胜达,秦永松.Markov随机环境过程驱动的风险过程[J].广西师范大学学报(自然科学版),2012,30(1):35-39.DOI:10.16088/j.issn.1001-6600.2012.01.016.
[6]LATOUCHE G,RAMASWAMI V.Introduction to matrix analytic methods in stochastic modeling[M].Phladelphia,PA:SIAM,1999.
[7]ASMUSSEN S.Stationary distributions via first passage times[C]//DSHALALOW J H.Advances in Queueing:Theory,Methods,and Open Problems.Boca Raton,FL:CRC Press,1995:79-102.
[8]BADESCU A L,BREUER L,Da SILVA SOARES A,et al.Risk processes analyzed as fluid queues[J].Scand Actuar J,2005,2005(2):127-141.DOI:10.1080/03461230410000565.
[9]BADESCU A L,LANDRIAULT D.Applications of fluid flow matrix analytic methods in ruin theory:a review[J].Rev R Acad Cien Serie A Mat,2009,103(2):353-372.DOI:10.1007/BF03191912.
[10]RAMASWAMI V.Passage times in fluid models with application to risk processes[J].Methodol Comput Appl Probab,2006,8(4):497-515.DOI:10.1007/s11009-006-0426-9.
[11]RAMASWAMI V.Matrix analytic methods for stochastic fluid flows[C]//Proceedings of the 16th International Teletraffic Congress.Edinburgh:ITC,1999:1019-1030.
[12]BEAN N G,O’REILLY M M,TAYLOR P G.Algorithms for the Laplace-Stieltjes transforms of first return times for stochastic fluid flows[J].Methodology and Computing in Applied Probability,2008,10(3):381-408.DOI:10.1007/s11009-008-9077-3.
[13]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.DOI:10.13546/j.cnki.tjyjc.2015.21.005.
[14]BEAN N G,O’REILLY M M,TAYLOR P G.Hitting probabilities and hitting times for stochastic fluid flows:the bounded model[J].Probability in the Engineering and Informational Sciences,2009,23(1):121-147.DOI:10.1017/S0269964809000102.
[15]ABATE J,WHITT W.Numerical inversion of Laplace transforms of probability distributions[J].ORSA Journal on Computing,1995,7(1):36-43.DOI:10.1287/ijoc.7.1.36.