Extreme values and robustness

极值和鲁棒性

• 批准号: 170049-2009
• 负责人: Dupuis, Debbie
• 金额: $ 1.38万
• 依托单位: HEC Montréal
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=569537
• 关键词: Extreme; values; robustness

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.

极端情况的随机建模对于许多领域都很重要。当许多结构设计依赖于基于数据的方法来估计设计载荷时，估计洪水、大风、大降水（雨、雪或冰）等的发生率和严重程度对于工程至关重要。 低估可能的极端载荷会导致灾难性的结构失效；回想一下冰暴过后输电塔的状态。 这一建模领域在保险和金融领域也很重要。 保险公司可能面临大额（灾难性）索赔，而公司的偿付能力主要取决于大额索赔的规模和频率。最近发生的环境灾难（例如安德鲁飓风、密西西比洪水、1998 年冰暴和卡特里娜飓风）给保险业带来了严重破坏并最终造成财务破产，这一问题非常现实。在金融市场上，大幅价格变动很少见，但很重要。我们回想起1987年10月的市场下跌，而2008年10月的下跌我们还没有找到底部。每日股市指数波动性的增加引起了从业者和研究人员的广泛关注。由于意外的市场波动，公司（和个人）遭受了巨大损失。我们需要准确衡量市场和保险风险，这需要对大额损失和索赔的分布进行准确建模。 许多人一致认为该领域缺乏实用的统计方法。过去几年已经取得了一些进展：考虑非平稳性和相关性的更现实的模型；适度的多元模型可以更好地利用可用数据；贝叶斯分析结合了“专家”知识；以及识别和降低“小”极端值的稳健模型（减少低估）。 然而，还有很长的路要走。 拟议研究的目的是进一步推进这些最新方法所取得的进展并开发新方法。