expected shortfall, measuring the average outcome (e.g., portfolio loss) above a given quantile
of its probability distribution, is a common financial risk measure. the same measure can be
used to characterize treatment effects in the tail of an outcome distribution, with applications
ranging from policy evaluation in economics and public health to biomedical investigations.
expected shortfall regression is a natural approach of modeling covariate-adjusted expected
shortfalls. because the expected shortfall cannot be written as a solution of an expected loss
function at the population level, computational as well as statistical challenges around
expected shortfall regression have led to stimulating research. we discuss some recent
developments in this area, with a focus on a new optimization-based semiparametric approach
to estimation of conditional expected shortfall that adapts well to data heterogeneity with
minimal model assumptions.