Extreme values and robustness

极值的随机建模在许多领域都具有重要意义。当许多结构设计依赖于基于数据的方法来估计设计荷载时，对洪水、大风、大降水(雨、雪或冰)等的发生和严重程度的估计对于工程来说是必不可少的。低估可能的极端载荷会导致灾难性的结构故障；回想一下冰暴过后输电塔的状态。 这一领域的建模在保险和金融领域也很重要。保险公司可能面临巨额(灾难性的)索赔，而一家公司的偿付能力关键取决于巨额索赔的规模和频率。这个问题在最近的环境灾难中是非常真实的，例如飓风安德鲁、密西西比州洪水、1998年冰暴和飓风卡特里娜给保险业造成了严重破坏和最终的财务失败。在金融市场上，价格大幅波动是罕见的，但很重要。我们回忆起1987年10月的市场下跌，我们还没有在2008年10月的下跌中找到底部。每日股市指数波动性的增加引起了实践者和研究者的广泛关注。由于意外的市场波动，公司(和个人)承受了巨大的损失。我们需要准确衡量市场和保险风险，这需要对巨额损失和索赔的分布进行准确建模。 许多人同意，在这一领域缺乏实用的统计方法。过去几年取得了一些进展：考虑到非平稳性和相关性的更现实的模型；更好地利用现有数据的适度多变量模型；纳入“专家”知识的贝叶斯分析；以及识别和减轻“小”极端的稳健模型(减少低估)。然而，还有很长的路要走。拟议研究的目的是促进这些最新方法所取得的进展，并开发新的方法。

The stochastic modeling of extremes is important to many fields. Estimation of the incidence and severity of floods, large winds, large precipitations (rain, snow, or ice), and so on are essential to engineering when many structural designs rely on data-based methodologies for the estimation of design loads. Underestimation of probable extreme loads leads to catastrophic structural failure; recall the state of the transmission towers after the Ice Storms. This area of modeling is also important in insurance and finance. Insurance companies face probable large (catastrophic) claims and a company's solvency depends critically on the size and the frequency of large claims. The issue is very real with recent environmental disasters such as Hurricane Andrew, the Mississippi floods, the 1998 Ice Storms, and Hurricane Katrina causing havoc and eventual financial failures in the insurance industry. On the financial markets, large price movements are rare, but important. We recall the October 1987 market drop, and we have yet to find the bottom in the October 2008 drop. Increases in volatility of daily stock market indices have attracted much attention from both practitioners and researchers. Companies (and individuals) have taken on huge losses due to unexpected market moves. We need accurate measures of market and insurance risks and that requires accurate modeling of the distribution of large losses and claims. Many agree that there is a lack of practical statistical methodology in this area. Some progress has been made in the last few years: more realistic models accounting for non-stationarity and correlation; modest multivariate models making better use of available data; Bayesian analyses incorporating ''expert'' knowledge; and robust models identifying and downweighting ''small'' extremes (reducing underestimation). However, there is still a long way to go. The purpose of the proposed research is to further the progress made by these recent methodologies and develop new methods.