贝叶斯方法下半参数混合模型在极端值的应用研究

发布时间：2018-08-09 19:38

【摘要】：极端稀有事件具有概率小、损失强度高等特征,其事故的发生会造成大量直接或者间接的经济损失,严重威胁着保险公司的稳定经营。因此,对极端稀有事件的准确预测尤为重要。目前,对极端稀有事件预测广泛采用的方法是极值理论,然而极值理论对阈值的选取极为敏感,且是使用者主观的判断,与此同时,极值理论无法对估计出来的参数进行评估,无法了解参数的统计特征,更不能得到参数的置信区间。而贝叶斯方法能够很好的解决这个问题。本文在极值理论的基础上,提出分段相加的半参数混合模型,阈值以下采用的是属于数值逼近范畴的半参数模型,阈值以上部分采用的是广义帕累托(GPD)分布。广义帕累托模型在估计稀有事件的极端分位点有很重要的作用,特别是对重尾损失的拟合准确度很高。本文运用贝叶斯方法建模,选择合适的参数先验分布,结合似然函数,推断出混合模型的后验分布,再使用马尔可夫蒙特卡洛(MCMC)对后验分布进行抽样,得到各个参数的频率分布图,再通过抽样的结果得到参数的统计特征。在选择阈值以下部分的模型时,本文选用的是半参数模型。半参数模型是数值逼近的方法,理论较为成熟,在国内外也有比较广泛的应用,但已有的研究中并没有运用到贝叶斯估计中,也没有与极值理论相结合使用的情况。因此本文在损失评估研究中引入半参数模型以实现更为精确的预测结果。理论上能够有效的改进当前流行的极值理论和参数混合模型的方法,实证结果表明,半参数模型对阈值以下部分的拟合效果要优于参数模型,最终对损失分布的预测结果也更合理,且这也为尖峰厚尾数据集的分位点预测提供了一条改进的途径。因此,本文提高了对尖峰厚尾损失评估的准确性,为损失预测提供了新的途径。
[Abstract]:Extreme rare events have the characteristics of small probability and high loss intensity. The occurrence of their accidents will cause a large number of direct or indirect economic losses, which seriously threaten the stable operation of insurance companies. Therefore, the accurate prediction of extreme rare events is particularly important. At present, the method widely used for extreme rare event prediction is the extreme value theory, but The extreme value theory is very sensitive to the selection of the threshold, and it is the subjective judgment of the user. At the same time, the extremum theory can not evaluate the estimated parameters, can not understand the statistical characteristics of the parameters, and can not get the confidence interval of the parameters, but the Bayesian method can solve the problem well. This paper is based on the basis of extreme value theory. In this paper, a semi parametric hybrid model with piecewise addition is proposed. The threshold below is a semi parametric model which belongs to the category of numerical approximation. The above threshold is used in the generalized Pareto (GPD) distribution. The generalized Pareto model plays an important role in estimating the extreme subloci of rare events, especially for the fitting accuracy of heavy tail loss. In this paper, the Bayesian method is used to model, select the appropriate prior distribution of parameters, combine the likelihood function, deduce the posterior distribution of the mixed model, and then use Markov Montecarlo (MCMC) to sample the posterior distribution, get the frequency distribution map of the parameters, and then pass the sampling results to get the statistical characteristics of the parameters. In the selection of the threshold value, the threshold is selected. The semi parametric model is used in the following part of the model. The semi parametric model is a numerical approximation method. The theory is more mature and has a wide range of applications at home and abroad. However, the existing research has not been used in the Bayesian estimation and is not used in combination with the extreme value theory. Therefore, this paper is in the loss assessment study. The semi parametric model is introduced to achieve more accurate prediction results. In theory, the current popular extremum theory and parameter mixed model can be effectively improved. The empirical results show that the semi parametric model is better than the parameter model for the fitting effect of the lower part of the threshold. Finally, the prediction results of the loss distribution are more reasonable, and this is also the case. It provides an improved way for the prediction of the pinnacle thick tail data set. Therefore, this paper improves the accuracy of the peak tailing loss assessment and provides a new way for the loss prediction.
【学位授予单位】：湖南大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：F224;F840.4

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