Random variables that stand for cost, loss or damage must be confronted in numerous
situations. Dealing with them systematically for purposes in risk management, optimization …

We introduce the method of Geodesic Principal Component Analysis (GPCA) on the space
of probability measures on the line, with finite second moment, endowed with the …

Conditional value-at-risk (CVaR) and value-at-risk, also called the superquantile and
quantile, are frequently used to characterize the tails of probability distributions and are …

Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals with non-
smooth Riesz kernels show a rich structure as singular measures can become absolutely …

Engineering decisions are invariably made under substantial uncertainty about current and
future system cost and response, including cost and response associated with low …

The paper presents a generalized regression technique centered on a superquantile (also
called conditional value-at-risk) that is consistent with that coherent measure of risk and …

Spectral risk objectives–also called L-risks–allow for learning systems to interpolate
between optimizing average-case performance (as in empirical risk minimization) and worst …

This paper studies a probabilistic characteristic called buffered probability of exceedance
(bPOE). It is a function of a random variable and a real-valued threshold. By definition, bPOE …

R. Tyrell Rockafellar and his collaborators introduced, in a series of works, new regression
modeling methods based on the notion of superquantile (or conditional value-at-risk). These …

We consider the problem of optimizing the structure of sown areas, taking into account the
risk of crop losses. To minimize the risk, we propose to optimize the buffered probability of …