This paper surveys the most recent advances in the context of decision making under
uncertainty, with an emphasis on the modeling of risk-averse preferences using the …

Conic optimization is a significant and thriving research area within the optimization
community. Conic optimization is the general class of problems concerned with optimizing a …

The quantification of downside risk in terms of capital requirements is a key issue for both
regulators and the financial industry. This review presents the axiomatic approach, which is …

This book gives an introduction to basic concepts and methods in mathematical risk
analysis, in particular to those parts of risk theory which are of particular relevance in finance …

We address the problem of risk sharing among agents using a two-parameter class of
quantile-based risk measures, the so-called range-value-at-risk (RVaR), as their …

S. Kusuoka [KOI, Theorem 4] gave an interesting dual characterization of law invariant
coherent risk measures, satisfying the Fatou property. The latter property was introduced by …

Coherent, convex, and monetary risk measures were introduced in a setup where uncertain
outcomes are modeled by bounded random variables. In this paper, we study such risk …

We consider the problem of optimal risk sharing of some given total risk between two
economic agents characterized by law‐invariant monetary utility functions or equivalently …

We show that the only dynamic risk measure which is law invariant, time consistent and
relevant is the entropic one. Moreover, a real valued function c on L∞(a, b) is normalized …

When there is uncertainty about interest rates (typically due to either illiquidity or
defaultability of zero coupon bonds) the cash‐additivity assumption on risk measures …