Collaborative Proposal: Models and Methods for High Quantiles in Risk Quantification and Management

近年来，金融市场、经济和公共卫生方面的脆弱性对社会构成了日益严重的风险。为了监测自然灾害和预测流行病，金融机构和政府组织必须投资于风险情报，以便清楚地界定、理解、衡量、量化和管理它们对风险的容忍度和风险敞口。通过采用严格而稳健的分析方法来衡量、量化和预测风险，商业领袖和监管者可以更少地依赖直觉，更多地依靠系统的方法来管理风险并做出合理的政策决策。该项目将为应用研究人员、监管机构和从业人员开发改进的、强大的分析工具来进行风险评估。这些工具和技术将在经济、金融和保险等广泛领域产生广泛影响。该项目还打算为研究生提供培训机会，并扩大代表性不足的群体对统计和精算科学的参与。本研究项目主要针对数学模型计算的条件和无条件风险度量进行不确定性量化、回测和敏感性分析。该项目为ARMA-GARCH模型开发了一种计算效率高的两步推理，并将参数和半参数分布族拟合到残差中。研究人员将研究半监督学习风险分析时，其他变量与大样本量是可用的。他们还计划验证基于残差的自举方法，用于量化风险不确定性，并开发有效的风险预测和反向测试方法。新方法结合了一些现代统计技术，如预测灾难性风险的极值理论，处理无限方差和持续波动的加权估计，以及有效假设检验的经验似然法。这些技术具有鲁棒性，适用于风险管理和其他需要不确定性量化的研究领域的各种问题。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

In recent years, vulnerabilities in financial markets, economies, and public health have posed increasingly severe risks to society. For monitoring natural disasters and forecasting epidemics, financial institutions and governmental organizations must invest in risk intelligence to clearly define, understand, measure, quantify, and manage their tolerance for and exposure to risk. By employing rigorous and robust analytics to measure, quantify, and forecast risk, business leaders and regulators can rely less on intuition and more on systematic methodologies to manage risk well and make sound policy decisions. This project will develop improved and powerful analytic tools for applied researchers, regulators, and practitioners to conduct risk assessment. These tools and techniques will have broad impacts in wide-ranging fields such as economics, finance, and insurance. The project also intends to provide training opportunities for graduate students and broaden the participation of underrepresented groups in statistics and actuarial science. This research project focuses on the uncertainty quantification, back-test, and sensitivity analysis for both conditional and unconditional risk measures computed from mathematical models. This project develops a computationally efficient two-step inference for an ARMA-GARCH model and fits parametric and semi-parametric distribution family to residuals. The investigators will study semi-supervised learning for risk analysis when other variables with a large sample size are available. They also plan to validate residual-based bootstrap methods for quantifying risk uncertainty and develop efficient ways for risk forecasts and back-tests. The new methodologies combine some modern statistical techniques such as extreme value theory for forecasting catastrophic risk, weighted estimation for handling both infinite variance and persistent volatility, and empirical likelihood method for efficient hypothesis testing. These techniques are robust and applicable to various problems in risk management and other research fields requiring uncertainty quantification.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.