Collaborative Research: Modeling and Analyzing Extreme Risks in Insurance and Finance

合作研究：保险和金融极端风险的建模和分析

• 批准号: 1436700
• 负责人: Jose Blanchet
• 金额: $ 13.78万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2014
• 资助国家: 美国
• 起止时间: 2014-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1436700&HistoricalAwards=false
• 关键词: Collaborative; Research; Modeling; Analyzing; Extreme

Recent rare events with disastrous economic and social consequences, so-called Black-Swan events, have made today's world far different from just decades ago. Examples of these events range from earthquakes and nuclear crises to the collapse of financial market from sub-prime mortgages. All of these intensify the need for risk management among the insurance and financial industry, and in particular, the invention of new tools to model, analyze, predict, and manage extreme risks. The investigators will undertake the fundamental challenges posed by the study of rare events: they, by nature, are short of data, their likelihood is difficult to compute, and that they are difficult to reflect via accurate models. As such, the investigators will take an integrated approach that combines statistical methods, probabilistic analysis, optimization, and efficient computer simulation to assess their risks. The research has potential for high societal impact, given the wide range of applications of the models and methods documented in the project for handling the important implications of extreme events. The investigators plan to train several Ph.D. students and will also involve them in K12 education as guest lecturers via Harlem Schools Partnership with Columbia University. The investigators will attempt to recruit high-quality personnel from under-represented groups. They will also disseminate the scientific output of this project via open access sites.The intellectual strength of the project rests on the fact that it includes algorithmic, computational, statistical, and theoretical components. The goal is to establish a robust and systematic approach for modeling and analyzing extreme risks in insurance and finance. The investigators systematically combine: a) the theory of extreme value statistics, b) asymptotic analysis in probability, c) stochastic optimization, and d) highly efficient Monte Carlo techniques. Specific objectives include: 1) establishing a robust asymptotic theory to account for tail events uniformly over a wide range of settings, 2) taking advantage of the asymptotic large deviations theory to build provably efficient Monte Carlo estimators for rare events, and 3) investigation of a robust optimization approach that accounts for model misspecification. The investigators' approach is both innovative and necessary because the nature of rare events exposes deficiencies in each of these areas: i) The theory of extreme value statistics assumes a large number of data points to provide accurate estimators but the nature of rare events precludes this assumption. ii) Asymptotic analysis techniques allow to obtain formulas that are easily evaluated and thus amenable to sensitivity analysis under a wide range of model parameters. So, asymptotics may help mitigate some of the statistical error issue, but unfortunately, they carry an unmeasurable error and often lose important information. iii) Efficient Monte Carlo has a controlled error by sampling, but it still assumes a model in place and could lead to incorrect conclusions in case the model is incorrect. iv) Optimization techniques might help mitigate the problem of model uncertainty by computing bounds for the probabilities of interest, optimizing over the selection of models that cover the truth with high confidence. However, these might be too loose to be practical or the optimization problem could be too complex, thus the need from 1) to 3). Overall, the investigators will establish a comprehensive approach that resolves the deficiencies exposed by each of the aforementioned segregated methods.

最近遇到灾难性的经济和社会后果的罕见事件，即所谓的黑人事件，使当今的世界与几十年前的不同之处有很大不同。这些事件的例子从地震和核危机到金融市场的崩溃。所有这些都加剧了保险和金融行业之间对风险管理的需求，尤其是发明了新工具来建模，分析，预测和管理极端风险。研究人员将面临罕见事件的研究带来的基本挑战：他们本质上是缺乏数据，他们的可能性很难计算，并且很难通过准确的模型来反映。因此，研究人员将采用一种结合统计方法，概率分析，优化和有效计算机模拟的综合方法，以评估其风险。鉴于项目中记录在处理极端事件的重要含义的模型和方法的广泛应用，这项研究具有高社会影响的潜力。调查人员计划培训几位博士学位学生，还将通过哈林学校与哥伦比亚大学合作作为客座讲师参加K12教育。调查人员将尝试从代表性不足的群体中招募高质量的人员。他们还将通过开放访问站点传播该项目的科学输出。项目的智力强度取决于它包括算法，计算，统计和理论组件。目的是建立一种强大而系统的方法来建模和分析保险和金融中的极端风险。研究人员系统地结合了：a）极值统计的理论，b）概率中的渐近分析，c）随机优化和d）高效的蒙特卡洛技术。具体目标包括：1）建立强大的渐近理论，以在广泛的环境中统一地解释尾巴事件，2）利用渐近的大偏差理论，以构建可证明有效的蒙特卡洛估计器，以实现罕见事件，3）研究可构成模型错误的强大优化方法。研究人员的方法既具有创新性，又是必要的，因为罕见事件的性质暴露了每个领域的缺陷：i）极值统计的理论假设大量数据点可以提供准确的估计器，但罕见事件的性质阻止了这一假设。 ii）渐近分析技术允许获得易于评估的公式，因此可以在广泛的模型参数下进行灵敏度分析。因此，渐近学可能有助于减轻某些统计错误问题，但不幸的是，它们带有无法衡量的错误并经常失去重要信息。 iii）有效的蒙特卡洛（Monte Carlo）通过采样具有控制误差，但它仍然假定模型已经到位，并且如果模型不正确，则可能导致不正确的结论。 iv）优化技术可以通过计算感兴趣的概率来计算界限，以高度置信度覆盖真相的模型，从而有助于减轻模型不确定性问题。但是，这些可能太松了，无法实用，或者优化问题可能太复杂了，因此需要从1）到3）。 总体而言，研究人员将建立一种全面的方法，以解决上述每种隔离方法暴露的缺陷。