一类马氏到达过程的实质破产问题

The bankruptcy problem of markov arrival process

破产问题是金融保险研究的重要问题之一。针对Markov到达过程环境下的破产模型,考虑了它的实质破产问题。根据索赔发生,实质破产发生和环境状态改变3个因素,利用重期望公式得到Markov环境中在不同初始盈余下实质破产所满足的积分微分方程。进一步求得了一维环境状态与二维环境状态时带有破产率函数的实质破产概率表达式,并且给出了常值破产率函数下的实质破产概率与特殊数值解。

Thebankruptcy problem was one of the important problems in the financial and insurance,and it was considered in this paper by the aid of the model of Markov arrival process.The double expectation formula was used to derive integra-differential equations of the bankruptcy underdifferent initial surplus on Markov arrival process,with each corresponding to different factorssuch as occurrence of claim,occurrence of bankruptcy and the change of environment state.Furthermore,the expression for the bankruptcy probability with bankruptcy rate functionwere also derived for both cases of one and two states.Whenthe bankruptcy rate function is constant,the bankruptcy probability was given andspecial numerical solution was presented.