带标准Brown运动扰动风险模型的破产概率模拟计算  

Simulation of Ruin Probability for the Risk Model Perturbed by the Standard Brown Motion

作　　者：王琪 薛红[1] 陈毛毛 WANG Qi;XUE Hong;CHEN Maomao(School of Science,Xi’an Polytechnic University,Xi’an 710600,China)

机构地区：[1]西安工程大学理学院

出　　处：《四川理工学院学报（自然科学版）》2019年第6期82-89,共8页Journal of Sichuan University of Science & Engineering(Natural Science Edition)

基　　金：国家自然科学基金(11601410);陕西省自然科学基础研究计划(2016JM1031);中国博士后科学基金(2017M613169)

摘　　要：当索赔额序列服从重尾分布时,带标准Brown运动扰动风险模型的破产概率无解析表达式。首先提出一种模拟带标准Brown运动扰动风险模型盈余轨道的程序思想,结合Monte-Carlo方法,讨论风险模型在有限时间内的破产概率,并通过数值算例验证了程序的有效性。其次根据中国太平洋财产保险股份有限公司2014年和2015年的数据,利用统计分析方法,采用广义Pareto分布刻画重大理赔额序列,Poisson过程刻画理赔次数,标准Brown运动刻画其它风险干扰因素。最后对该公司有限时间内的破产概率进行了Monte-Carlo模拟计算。由于综合考虑了其他营业支出及风险干扰等影响因素,使得保险公司在有限时间内的破产概率模拟计算结果更加贴合实际。When the claim sizes follow the heavy-tailed distribution, there is no analytic expression for the ruin probability of the risk model perturbed by the standard Brown motion. First, a Programming thought is proposed to simulate the surplus process path of the risk model perturbed by the standard Brown motion. Combining the Monte-Carlo simulation algorithm, the ruin probability in finite time of the risk model is studied, and the effectiveness of the program is verified by numerical examples. After that, statistical methods are used to analyze the relevant data from China Pacific Property Insurance Company in 2014 and 2015. The claim sizes obey generalized Pareto distribution, and the number of claims follows a Poisson process. We use the standard Brown motion to characterize some risk factors which include small claims events and office expenses. Finally the Monte-Carlo simulation of the company’s ruin probability in finite time are obtained.Considering factors such as operating expenses and risk interference, so the simulation results are more practical.

关 键 词：带标准Brown运动扰动风险模型 Monte-Carlo数值模拟 有限时间破产概率 

分 类 号：F830[经济管理—金融学] O211[理学—概率论与数理统计]