一类马氏调制风险模型的破产概率

本文研究一类马氏调制风险模型的破产概率,在此模型中索赔到达间隔和索赔额都受一外在马氏过程的影响,保费收入则受该外在的马氏过程和公司的储备金水平的影响.本文不仅考虑了随机环境对保险公司的影响,而且考虑了保险公司为了吸引新的顾客,会根据储备金的水平来调整保费收入.因此所考虑的保险模型更加贴近现实,更加易于应用.通过向后微分讨论,根据外在过程的马氏性,严格推导出破产概率所满足的积分方程.进一步,通过拉普拉斯变换的方法,给出了积分方程的解.最后,给出一个例子来展示所得结果的可行性和有效性.

The Probability of Ruin in a kind of Markov-modulated Risk Model

In this paper, the probability of ruin is investigated in a Markov-modulated risk model,in which the claim inter-arrives and claim sizes are influenced by an external Markovian process, and the premium rate depends on the external Markovian process and the level of company's reserves. We consider not only that stochastic environment would influence the insurance company, but also that the insurance company would adjust premium according to the level of reserves to attract new customers. So the risk model is closer to reality and more accessible to apply. By using the backward differential argument and the Markov property of the external process, we derive the integral equation satisfied by the probability of ruin. Further, we solve the equation by Laplace transforms. Finally, an example is given to illustrate the feasibility and effectiveness of the obtained theoretical results.