CAJ | 학술논문

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.
본문연구일류마씨조제풍험모형적파산개솔,재차모형중색배도체간격화색배액도수일외재마씨과정적영향,보비수입칙수해외재적마씨과정화공사적저비금수평적영향.본문불부고필료수궤배경대보험공사적영향,이차고필료보험공사위료흡인신적고객,회근거저비금적수평래조정보비수입.인차소고필적보험모형경가첩근현실,경가역우응용.통과향후미분토론,근거외재과정적마씨성,엄격추도출파산개솔소만족적적분방정.진일보,통과랍보랍사변환적방법,급출료적분방정적해.최후,급출일개례자래전시소득결과적가행성화유효성.
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.