Estimating Risk Measures, with Applications to Finance and Nuclear Safety

这项研究补助金将通过设计和研究有效的风险评估计算方法，促进国家基础设施的安全和金融机构的稳定，其目标是将目前使用的方法的统计误差减少几个数量级。该项目特别考虑了核电站的风险分析，其中工程师通过假设事故的计算模型进行概率风险评估，以及金融机构确定适当的资本水平以防止不可预见的巨大未来损失的方法。由于这种情况下的风险度量通常与极其罕见的事件有关，因此模拟方法必须应用有效的方差减小技术，否则产生的估计器将遭受不可用的大采样误差。与当地高中的接触将有助于吸引学生从事STEM职业，这对我们国家未来的安全和繁荣至关重要。本项目的目标是建立蒙特卡罗和随机拟蒙特卡罗风险测度估计的严格数学性质，如风险值、条件风险值及其均值调整对应项。这项工作将描述大型复杂随机模型中估计器效率的极限行为，这些模型涉及依赖关系和非相同分布的输入。由于计算技术产生具有抽样误差的估计量，该项目通过可计算的误差界限和具有数学证明的理想渐近特征的置信区间提供不确定性量化。分析工作将与实际中出现的大规模随机模型的数值实验相辅相成。本项目旨在设计和分析各种蒙特卡罗和随机准蒙特卡罗方法，以有效地估计在不同应用领域采用的风险措施。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。

This research grant will contribute to the safety of national infrastructures and the stability of financial institutions by devising and studying efficient computational methods for risk assessment, with the goal of reducing statistical errors of currently used methodologies by orders of magnitude. The project specifically considers the risk analysis of nuclear power plants, where engineers conduct probabilistic risk assessments through computational models of hypothesized accidents, as well as methods for financial institutions to determine appropriate capital levels to protect against unforeseen large future losses. As risk measures in this context often relate to exceedingly rare events, simulation methods must apply effective variance-reduction techniques, without which the resulting estimators suffer from unusably large sampling errors. Outreach to local high schools will help attract students into pursuing STEM careers, which is vital to our nation’s future security and prosperity.The objective of this project is to establish rigorous mathematical properties of Monte Carlo and randomized quasi-Monte Carlo estimators of risk measures, such as the value-at-risk, the conditional value-at-risk, and their mean-adjusted counterparts. This work will characterize the limiting behavior of the estimators’ efficiencies for large and complex stochastic models, which involve dependencies and non-identically distributed inputs. As the computational techniques produce estimators with sampling error, the project provides uncertainty quantification via computable error bounds and confidence intervals with mathematically proven desirable asymptotic characteristics. The analytical work will be complemented with numerical experiments on large-scale stochastic models arising in practice.This project aims to devise and analyze various Monte Carlo and randomized quasi-Monte Carlo methods for efficiently estimating risk measures employed across different application areas.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.