分数Brown运动扰动风险模型的破产概率模拟计算

Simulation of Ruin Probability for Risk Model Perturbed by Fractional Brown Motion

分数Brown运动具有长程相依性,且已被应用于风险理论研究。考虑到现实中保险公司盈余过程序列具有长程相依性,建立分数Brown运动扰动风险模型来刻画盈余过程序列,并对有限时破产概率进行了Monte-Carlo模拟计算。结合Cholesky分解方法模拟分数Brown运动样本轨道;提出一种有效的数值模拟算法对有限时破产概率进行了模拟计算,并通过数值算例研究了Hurst指数和波动系数对破产概率的影响;结合中国太平洋财产保险股份有限公司在2008—2017年间的数据进行实证分析,从而根据有限时破产概率的数值模拟结果分析保险公司的运营状况。

Fractional Brown motion has the property of long-range correlation and has been used in risk theory.Considering the surplus process series of insurance company has long-range correlation in reality,the risk model perturbed by the fractional Brown motion is built to capture the surplus process series.And the Monte-Carlo simulations of the ruin probability in finite time are obtained.First,the Cholesky decomposition is used to simulate the simple path of fractional Brown motion.After that,an effective numerical algorithm is designed to simulate the ruin probability in finite time of the risk model.At the same time,the influences of Hurst exponent and volatility coefficient on the ruin probability are studied by numerical examples.Finally an empirical analysis is studied by using the data of China Pacific Property Insurance Company from 2008 to 2017.According to the numerical simulations of the company’s ruin probability in finite time,the operation of the company is also analyzed.