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给社会带来了越来越严重的风险。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，以明确定义、了解、衡量、量化和管理其对风险的容忍度和风险暴露。通过使用严谨可靠的分析来衡量、量化和预测风险，企业领导人和监管机构可以减少对直觉的依赖，而更多地依赖系统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、监管机构和从业者开发改进和强大的分析工具，以进行风险评估。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，并扩大任职人数不足的群体对统计和精算学的参与。本研究主要针对由数学模型计算出的条件风险与无条件风险进行不确定性量化、回溯检验及敏感性分析。该项目为ARMA-GARCH模型开发了一种计算高效的两步推断，并将参数和半参数分布族与残差相匹配。当有其他大样本变量时，研究人员将研究用于风险分析的半监督学习。他们还计划验证基于残差的Bootstrap方法，以量化风险不确定性，并开发有效的风险预测和回测方法。新的方法结合了一些现代统计技术，如用于预测巨灾风险的极值理论，用于处理无限方差和持续波动的加权估计，以及用于有效假设检验的经验似然方法。这些技术是稳健的，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NSF的法定使命，并通过使用基金会的智力优势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.