Estimating Risk Measures, with Applications to Finance and Nuclear Safety

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.