基于POT-GPD模型的地震巨灾损失分布研究

Research on earthquake catastrophe loss distribution based on POT-GPD model

极值理论关注风险损失分布的尾部特征,通常用来分析概率罕见的事件,它可以依靠少量样本数据,在总体分布未知的情况下,得到总体分布中极值的变化情况,具有超越样本数据的估计能力。因此,基于GPD(generalized pareto distribution)分布的POT(peak over threshold)模型可更有效地利用有限的巨灾损失数据信息,从而成为极值理论当前的主流技术(以下简称,POT-GPD模型)。针对地震巨灾发生频率低、损失高、数据不足且具有厚尾性等特点,利用POT-GPD模型对我国1969年至2013年间的地震直接经济损失数据进行了统计建模;采用样本Hill图及区间筛选算法选取阈值,并对形状参数及尺度参数进行了估计。模型检验表明,POT-GPD模型对巨灾风险厚尾特点具有较好的拟合效果和拟合精度,为地震巨灾风险估计的建模及巨灾债券的定价提供了理论依据。

Extreme value theory is concerned with the tail characteristics of risk loss distribution. It is usually used to analyze the probability rare events, which can be used to obtain the variation of extreme value in the overall dis- tribution with small sample data, and has the estimating ability beyond the sample data. Therefore, the peaks over threshold（POT） model based on generalized pareto distribution（GPD） can more effectively use limited catastrophe loss data information, and is becoming the current mainstream technology （hereinafter referred to as POT-GPD model） of the extreme value theory. In this paper, in view of the characteristics of low frequency, high loss, insuf- ficient data and thick tall for earthquake catastrophe, the statistical model for earthquake direct economic loss data of China during the years 1969 -2013 was established using the POT-GPD model. Sample Hill plot and interval filtering algorithm was employed to select the threshold values, and the shape parameter and scale parameter was estimated. The model tests showed that, fitting effect and fitting accuracy of the POT - GPD model are good for catas- trophe risks with fat-tail features. This study can provide theoretical basis for modeling the earthquake catastrophe risk estimation and pricing the catastrophe bonds.