Events

Prof. Wenxin Zhou
Associate Professor
Department of Information and Decision Sciences
University of Illinois Chicago

Expected Shortfall (ES), also known as superquantile or Conditional Value-at-Risk, has been recognized as an important risk measure in economics and finance. In this talk, we consider a joint regression framework that simultaneously models the conditional quantile and ES of a response variable given a set of covariates, for which the state-of-the-art approach is based on minimizing a joint loss function that is non-differentiable and non-convex. Motivated by the idea of using orthogonal scores to reduce sensitivity to nuisance parameters, we study a two-step framework for fitting joint quantile and ES regression models nonparametrically over RKHSs and using deep neural networks. We establish a non-asymptotic theory for the proposed estimators, carefully characterizing the impact of quantile estimation without relying on sample splitting. For ES kernel ridge regression, we further propose a fast inference method to construct pointwise confidence bands. For NN-based ES regression, we introduce a Huberized estimator that is robust against heavy tails in the response distribution.  A Python package, quantes (https://pypi.org/project/quantes/), has been developed to implement various ES regression methods.