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

See all articles by Ruodu Wang

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Yunran Wei

Northern Illinois University; University of Waterloo - Department of Statistics and Actuarial Science

Gordon Willmot

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: June 7, 2019

Abstract

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

Wang, Ruodu and Wei, Yunran and Willmot, Gordon, Characterization, Robustness and Aggregation of Signed Choquet Integrals (June 7, 2019). Forthcoming in Mathematics of Operations Research, Available at SSRN: https://ssrn.com/abstract=2956962 or http://dx.doi.org/10.2139/ssrn.2956962

Ruodu Wang (Contact Author)

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Yunran Wei

Northern Illinois University ( email )

1425 W. Lincoln Hwy
Dekalb, IL 60115-2828
United States

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

Gordon Willmot

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1
Canada

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