Risk Analysis via Generalized Pareto Distributions
通过拟合广义帕累托分布到超过阈值的损失数据来计算风险价值，研究了阈值选择对最大似然估计渐近方差的影响，并提出了随机加权自助法用于区间估计，对金融和保险领域的风险管理有参考价值。
We compute the value-at-risk of financial losses by fitting a generalized Pareto distribution to exceedances over a threshold. Following the common practice of setting the threshold as high sample quantiles, we show that, for both independent observations and time-series data, the asymptotic variance for the maximum likelihood estimation depends on the choice of threshold, unlike the existing study of using a divergent threshold. We also propose a random weighted bootstrap method for the interval estimation of VaR, with critical values computed by the empirical distribution of the absolute differences between the bootstrapped estimators and the maximum likelihood estimator. While our asymptotic results unify the inference with nondivergent and divergent thresholds, the finite sample studies via simulation and application to real data show that the derived confidence intervals well cover the true VaR in insurance and finance.