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，洪水、大风、大降水（雨、雪或冰）等的发生率和严重程度的估计对工程至关重要。 低估可能的极端载荷会导致灾难性的结构故障;回想冰风暴后输电塔的状态。 这一建模领域在保险和金融领域也很重要。 保险公司面临可能的巨额（灾难性）索赔，公司的偿付能力主要取决于巨额索赔的规模和频率。这个问题是非常真实的与最近的环境灾害，如飓风安德鲁，密西西比洪水，1998年冰风暴，卡特里娜飓风造成破坏和最终的金融失败，在保险业。在金融市场上，大的价格波动是罕见的，但很重要。我们还记得1987年10月的市场下跌，我们还没有找到2008年10月下跌的底部。股票市场指数日波动率的增加引起了实践者和研究者的广泛关注。公司（和个人）由于意外的市场波动而遭受巨大损失。我们需要对市场和保险风险进行准确的衡量，这就需要对大额损失和索赔的分布进行准确的建模。 许多人同意，这一领域缺乏切实可行的统计方法。在过去几年中取得了一些进展：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;结合“专家"知识的贝叶斯分析;以及确定和降低”小"极端值的稳健模型（减少低估）。 然而，还有很长的路要走。 拟议的研究的目的是进一步的进展，这些最近的方法和开发新的方法。

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.