Characterization, Robustness and Aggregation of Signed Choquet Integrals
Forthcoming in Mathematics of Operations Research
38 Pages Posted: 24 Apr 2017 Last revised: 9 Jul 2019
Date Written: June 7, 2019
This article contains various results on a class of non-monotone law-invariant risk functionals, called the signed Choquet integrals. A functional characterization via comonotonic additivity is established, along with some theoretical properties including six equivalent conditions for a signed Choquet integral to be convex. We proceed to address two practical issues currently popular in risk management, namely, robustness (continuity) issues and risk aggregation with dependence uncertainty, for signed Choquet integrals. Our results generalize in several directions those in the literature of risk functionals. From the results obtained in this paper, we see that many profound and elegant mathematical results in the theory of risk measures hold for the general class of signed Choquet integrals; thus they do not rely on the assumption of monotonicity.
Keywords: comonotonicity, Choquet integrals, risk functionals, risk aggregation, robustness
JEL Classification: C6, D8, G00
Suggested Citation: Suggested Citation