关键词: 长程相依性, 分数Brown运动, Monte-Carlo模拟计算, 破产概率

Abstract:

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.

Key words: long-range correlation, fractional Brown motion, Monte-Carlo simulation, ruin probability