基于POT模型的巨灾损失分布拟合及风险度量

POT model and its application to simulate the catastrophe loss distribution and risk measurement

巨灾的频繁发生已引起了社会各界的高度关注。本文应用阈顶点模型(Peaks over threshold,POT)和广义帕累托分布(generalized pareto distribution,GPD),对我国1969—2012年间的地震直接经济损失数据进行拟合,利用不同方法探讨了最优阈值的选取问题,并采用极大似然法对GPD分布的参数进行了估计。经检验发现POT模型拟合巨灾风险厚尾部分的效果较好。文章还探索了POT模型在VaR上的应用,并提出用CVaR、PML这2种风险测度指标来改善VaR。最后利用复合泊松分布的可分解性及实际损失额在不同起赔点下具有的不同分布函数的事实,充分考虑了不同情况下纯保费的计算。

The frequent occurrence of catastrophe has received great concern in the community. In this paper, we use POT model and the distribution of GPD to fit the direct economic loss of the earthquake data from 1969 to 2012 in China. Different methods were used to study the optimal threshold selection problem, and the maximum likelihood method is adopted to estimate the GPD＇ s parameters. After inspection, we found that the POT model to the extreme rear of the fitting of data is relatively consistent. The article also explores the application of Van based on POT model and puts forward CVaR and PML to improve the index Van. Finally we use the decomposability of compound poisson distribution and the fact that actual losses under different compensate point has different distribution function, to give the pure premium calculation under different conditions.