Seminar by Dr. Yunran WEI from School of Mathematics and Statistics, Carleton University

We analyze the “convex level sets” (CxLS) property of risk functionals, which is a necessary condition for the notions of elicitability, identifiability and backtestability, popular in the recent statistics and risk management literature. We put the CxLS property in the multi-dimensional setting, with a special focus on signed Choquet integrals, a class of risk functionals that are generally not monotone or convex. We obtain two main analytical results in dimension one and dimension two, by characterizing the CxLS property of all one-dimensional signed Choquet integrals, and that of all two-dimensional signed Choquet integrals with a quantile component. The new findings generalize several results in the recent literature, and partially answer an open question on the characterization of multi-dimensional elicitability.

Dr. Wei is an Assistant Professor in the School of Mathematics and Statistics at Carleton University, Canada. She obtained her PhD in Actuarial Science from the University of Waterloo. Prior to joining Carleton University, she taught at the Northern Illinois University (USA). Her research interests include Quantitative Risk Management, Actuarial science, Decision Theory, Mathematical Finance, Operations Research and FinTech/InsurTech.