【摘要】：極端稀有事件具有概率小、損失強度高等特征,其事故的發(fā)生會造成大量直接或者間接的經(jīng)濟損失,嚴(yán)重威脅著保險公司的穩(wěn)定經(jīng)營。因此,對極端稀有事件的準(zhǔn)確預(yù)測尤為重要。目前,對極端稀有事件預(yù)測廣泛采用的方法是極值理論,然而極值理論對閾值的選取極為敏感,且是使用者主觀的判斷,與此同時,極值理論無法對估計出來的參數(shù)進(jìn)行評估,無法了解參數(shù)的統(tǒng)計特征,更不能得到參數(shù)的置信區(qū)間。而貝葉斯方法能夠很好的解決這個問題。本文在極值理論的基礎(chǔ)上,提出分段相加的半?yún)?shù)混合模型,閾值以下采用的是屬于數(shù)值逼近范疇的半?yún)?shù)模型,閾值以上部分采用的是廣義帕累托(GPD)分布。廣義帕累托模型在估計稀有事件的極端分位點有很重要的作用,特別是對重尾損失的擬合準(zhǔn)確度很高。本文運用貝葉斯方法建模,選擇合適的參數(shù)先驗分布,結(jié)合似然函數(shù),推斷出混合模型的后驗分布,再使用馬爾可夫蒙特卡洛(MCMC)對后驗分布進(jìn)行抽樣,得到各個參數(shù)的頻率分布圖,再通過抽樣的結(jié)果得到參數(shù)的統(tǒng)計特征。在選擇閾值以下部分的模型時,本文選用的是半?yún)?shù)模型。半?yún)?shù)模型是數(shù)值逼近的方法,理論較為成熟,在國內(nèi)外也有比較廣泛的應(yīng)用,但已有的研究中并沒有運用到貝葉斯估計中,也沒有與極值理論相結(jié)合使用的情況。因此本文在損失評估研究中引入半?yún)?shù)模型以實現(xiàn)更為精確的預(yù)測結(jié)果。理論上能夠有效的改進(jìn)當(dāng)前流行的極值理論和參數(shù)混合模型的方法,實證結(jié)果表明,半?yún)?shù)模型對閾值以下部分的擬合效果要優(yōu)于參數(shù)模型,最終對損失分布的預(yù)測結(jié)果也更合理,且這也為尖峰厚尾數(shù)據(jù)集的分位點預(yù)測提供了一條改進(jìn)的途徑。因此,本文提高了對尖峰厚尾損失評估的準(zhǔn)確性,為損失預(yù)測提供了新的途徑。
[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.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2016
【分類號】：F224;F840.4

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