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

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.