Estimating Risk Measures, with Applications to Finance and Nuclear Safety

评估风险措施，并应用于金融和核安全

• 批准号: 2345330
• 负责人: Marvin Nakayama
• 金额: $ 45.77万
• 依托单位: New Jersey Institute of Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-03-01 至 2027-02-28
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2345330&HistoricalAwards=false
• 关键词: Estimating; Risk; Measures; Applications; Finance

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.

这项研究赠款将通过设计和研究风险评估的有效计算方法，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，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资本水平的方法，以防止不可预见的未来巨大损失。 由于在这种情况下的风险措施往往涉及到非常罕见的事件，模拟方法必须采用有效的方差减少技术，没有它所产生的估计遭受不必要的大抽样误差。本项目的目标是建立风险度量的蒙特卡罗和随机准蒙特卡罗估计的严格数学性质，如风险价值，条件风险价值，以及它们的均值调整对应物。这项工作将描述大型和复杂的随机模型，其中涉及依赖性和非同分布的输入估计的效率的限制行为。由于计算技术产生的估计与抽样误差，该项目提供了不确定性量化通过可计算的误差范围和置信区间与数学证明可取的渐近特性。分析工作将辅以在实践中出现的大规模随机模型的数值实验。本项目旨在设计和分析各种Monte Carlo和随机准蒙特卡罗方法，用于有效地估计不同应用领域采用的风险措施。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查进行评估来支持的搜索.