The concepts of risk aversion, chance-constrained optimization, and robust optimization
have developed significantly over the last decade. The statistical learning community has …

The official history of copulas begins in 1959 with Sklar [1959]; but, as is often the case in
Mathematics, for groundbreaking results there are forerunners and precedents. These latter …

In this review paper we outline some recent contributions to copula theory. Several new
author's investigations are presented briefly, namely: order statistics copula, copulas with …

The latest tools and techniques for pricing and risk management This book introduces
readers to the use of copula functions to represent the dynamics of financial assets and risk …

Copula modeling has taken the world of finance and insurance, and well beyond, by storm.
Why is this? In this article, I review the early start of this development, discuss some …

In quantitative risk management, it is important and challenging to find sharp bounds for the
distribution of the sum of dependent risks with given marginal distributions, but an …

Extending the approach of Jouini, Meddeb, and Touzi [Finance Stoch., 8 (2004), pp. 531–
552] we define set-valued (convex) measures of risk and their acceptance sets, and we give …

We propose a nonlinear difference-in-differences (DiD) method to estimate multivariate
counterfactual distributions in classical treatment and control study designs with …

In this paper, we introduce two alternative extensions of the classical univariate Value-at-
Risk (VaR) in a multivariate setting. The two proposed multivariate VaR are vector-valued …

The class of distortion riskmetrics is defined through signed Choquet integrals, and it
includes many classic risk measures, deviation measures, and other functionals in the …