MArP风险过程破产时间的改进算法
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摘要
文章分析索赔服从PH分布下的MArP风险过程,提出这一风险过程破产时间的改进算法.即,将MArP风险过程转化为Markov流体队列(MFQ),基于Erlang分布,构造初始水平为0的MFQ序列,应用MFQ理论,得到了MArP风险过程破产时间的LST的趋近表示式,进而给出最终破产概率以及破产赤字分布的改进算法。
This paper analyzes the MArP risk process of claim being subject to PH distribution, and proposes an improved algorithm of this risk process. The paper transforms MArP risk process into a Markov Fluid Queue(MFQ) and based on Erlang distribution constructs a serial of MFQ with initial level as 0. And then the paper employs MFQ theory to obtain the approximation LST expressions of the ruin time, thus presenting the improved algorithm of the ultimate ruin probability and the distribution of deficit at ruin.
This paper analyzes the MArP risk process of claim being subject to PH distribution, and proposes an improved algorithm of this risk process. The paper transforms MArP risk process into a Markov Fluid Queue(MFQ) and based on Erlang distribution constructs a serial of MFQ with initial level as 0. And then the paper employs MFQ theory to obtain the approximation LST expressions of the ruin time, thus presenting the improved algorithm of the ultimate ruin probability and the distribution of deficit at ruin.
引文
[1]Latouche G,Ramaswami V.Introduction to Matrix Analytic Methodsin Stochastic Modeling[J].Technometrics,2012,43(3).
[2]Asmussen,Koole G.Marked Point Processes as Limits of MarkovianArrival Streams[J].Journal of Applied Probability,1993,l30(2).
[3]Ahn S,Ramaswami V.Efficient Algorithms for Transient Analysis ofStochastic Fluid Flow Models[J].Appl.Probab.,2005,42(2).
[4]Asmussen S.Stationary Distributions via First Passage Times[J].InAdvances in Queueing:Theory,Methods,and Open Problems,1995.
[5]张超权,刘晓辉.求解MAr P风险过程破产时间的新方法[J].统计与决策,2015,(21).
[6]Badescu A L,Breuer L,et al.Risk Processes Analyzed as FluidQueues[J].Scand.Actuar,2005,(15).
[7]Badescu A L,David L.Applications of Fluid Flow Matrix AnalyticMethods in Ruin Theory-A Review[J].Rev.R.Acad.Cerie A.Mat.2009,103(2).
[8]Ramaswami V.Passage Times in Fluid Models With Application toRisk Processes[J].Methodol.Comput.Appl.Probab.,2006,8(4).
[9]Tang S,Tan L.Erlangian Approximation to Finite Time Probability ofBlocking Time of Multi-class OBS Nodes[J].Photonic Network Com-munications,2015,30(2).
[10]Bhatia R,Rosenthal P.How and Why to Solve the Operator EquationAX-XB=Y[J].Bull Lond Math Soc,1997,(29).
[11]Asmussen S,Avram F,Usabel M.Erlangian Approximations for Fi-nite Time Ruin Probabilities[J].N Bulletin,2002,(32).
[12]Jagerman D L.An Inversion Technique for the Laplace Transform[J].Bell System Technical Journal,1982,61(8).
[13]Ramaswami V,Woolford D,Stanford D.The Erlangization Method forMarkovian Fluid Flows[J].Annals of Operations Research,2008,(160).
[2]Asmussen,Koole G.Marked Point Processes as Limits of MarkovianArrival Streams[J].Journal of Applied Probability,1993,l30(2).
[3]Ahn S,Ramaswami V.Efficient Algorithms for Transient Analysis ofStochastic Fluid Flow Models[J].Appl.Probab.,2005,42(2).
[4]Asmussen S.Stationary Distributions via First Passage Times[J].InAdvances in Queueing:Theory,Methods,and Open Problems,1995.
[5]张超权,刘晓辉.求解MAr P风险过程破产时间的新方法[J].统计与决策,2015,(21).
[6]Badescu A L,Breuer L,et al.Risk Processes Analyzed as FluidQueues[J].Scand.Actuar,2005,(15).
[7]Badescu A L,David L.Applications of Fluid Flow Matrix AnalyticMethods in Ruin Theory-A Review[J].Rev.R.Acad.Cerie A.Mat.2009,103(2).
[8]Ramaswami V.Passage Times in Fluid Models With Application toRisk Processes[J].Methodol.Comput.Appl.Probab.,2006,8(4).
[9]Tang S,Tan L.Erlangian Approximation to Finite Time Probability ofBlocking Time of Multi-class OBS Nodes[J].Photonic Network Com-munications,2015,30(2).
[10]Bhatia R,Rosenthal P.How and Why to Solve the Operator EquationAX-XB=Y[J].Bull Lond Math Soc,1997,(29).
[11]Asmussen S,Avram F,Usabel M.Erlangian Approximations for Fi-nite Time Ruin Probabilities[J].N Bulletin,2002,(32).
[12]Jagerman D L.An Inversion Technique for the Laplace Transform[J].Bell System Technical Journal,1982,61(8).
[13]Ramaswami V,Woolford D,Stanford D.The Erlangization Method forMarkovian Fluid Flows[J].Annals of Operations Research,2008,(160).