基于交叉熵的极端事件模拟研究

发布时间：2018-03-20 08:14

本文选题：极端事件　切入点：重要抽样(IS)　出处：《苏州大学》2015年硕士论文　论文类型：学位论文

【摘要】：极端事件是指发生概率很小的事件,广泛存在于金融、生物学、气象学等众多领域:估计该类事件发生的概率在实际中有重要的作用。提高极端事件模拟的速度和准确性的中心技术就是重要抽样,但对于复杂的密度函数最优的参数却很难获得。本文给出采用交叉熵距离最小的方法获得最优参数,从而估计出极端事件发生的概率。这篇文章中,我们首先介绍应用重要抽样法(Importance Sampling,简称IS)模拟极端事件的相关理论和应用。随后,介绍交叉熵(Cross Entropy,简称CE)的定义、方法以及性质,并使用R程序对算法进行实施,求得参数值验证其可行性。最后,分别对混合分布和重尾分布(以Pareto、Weibull分布为例)的极端事件模拟进行介绍和分析,结果表明:基于交叉熵的重要抽样法模拟极端事件优于传统的CMC(Crude Monte Carlo)方法。
[Abstract]:Extreme events are events that have a small probability of happening and are widespread in finance, biology, Meteorology and many other fields: estimating the probability of such events plays an important role in practice. The central technique to improve the speed and accuracy of extreme events simulation is important sampling. However, it is difficult to obtain the optimal parameters of complex density function. In this paper, the method of minimum cross-entropy distance is used to obtain the optimal parameters, and the probability of extreme events is estimated. In this paper, First, we introduce the theory and application of using important sampling method to simulate extreme events. Then, we introduce the definition, method and properties of cross entropy cross Entropy.The algorithm is implemented by using R program. Finally, the extreme event simulation of mixed distribution and heavy-tailed distribution (taking ParetoWeibull distribution as an example) is introduced and analyzed. The results show that the importance sampling method based on cross-entropy is superior to the traditional CMC(Crude Monte method in simulating extreme events.
【学位授予单位】：苏州大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O211

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