Markov调制风险模型的轨道刻划和概率构造  

Path-depict and Probabilistic Construction of the Markov-modulated Risk Model

作　　者：莫晓云[1,2] 杨向群[1] 

机构地区：[1]湖南师范大学数学与计算机科学学院,长沙410081 [2]湖南财政经济学院,长沙410205

出　　处：《应用数学学报》2012年第3期385-395,共11页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(No:11171101);高性能计算与随机信息处理省部共建教育部重点实验室(HPCsIP;湖南师范大学);教育部高校博士点基金(No:20104306110001);湖南省社科联基金(No:1011051B)资助项目

摘　　要：用随机过程的轨道,严格地刻划了Markov调制风险模型U=(Q,G,F;J,s,X),它是已有的Markov调制风险模型的一般化.基于模型U,分别给出带保费率向量C和带税率向量γ的Markov调制风险过程R^u={R^u(t),t≥0}和R^u(γ)={R^u(γ,t),t≥0}.给定特征组A=(Q,G,F),用概率方法构造了模型U.从而为用随机过程理论和方法研究Markov调制风险模型和过程,奠定了严实的随机过程基础.The Markov-modulated risk by using paths of stochastic processes,the model U = （Q, G, F; J, S, X） is precisely depicted model is vague generalization of available Markov- modulated risk models now. Based on the model U the Markov-modulated risk processes with premium-rate vector C and tax-vector 7, Ru= {Ru（t）, t≥0} and Ru（7） = {Ru（v, t）, t ≥0}, are given respectively. Let a characteristic group A = （Q, G, F） be given, the model U is constructed by using probabilistic method. It establishes a rigorous foundation of stochastic processes researching Markov-modulated risk models and Markov- modulated risk processes by using the theory and methods of stochastic processes.

关 键 词：MARKOV链 Q矩阵 带税率的Markov调制风险过程 轨道 概率构造 

分 类 号：O211.6[理学—概率论与数理统计]