Convex Risk Functionals: Representation and Applications

31 Pages Posted: 7 Aug 2018 Last revised: 22 Oct 2019

See all articles by Fangda Liu

Fangda Liu

University of Waterloo - Department of Statistics and Actuarial Science

Jun Cai

University of Waterloo - Department of Statistics and Actuarial Science

Christiane Lemieux

University of Waterloo - Department of Statistics and Actuarial Science

Ruodu Wang

University of Waterloo - Department of Statistics and Actuarial Science

Date Written: July 9, 2018

Abstract

We introduce the family of law-invariant convex risk functionals, which includes a wide majority of practically used convex risk measures and deviation measures. We obtain a unified representation theorem for this family of functionals. Two related optimization problems are studied. In the first application, we determine worst-case values of a law-invariant convex risk functional when the mean and a higher moment such as the variance of a risk are known. Second, we consider its application in optimal reinsurance design for an insurer. With the help of the representation theorem, we can show the existence and the form of optimal solutions.

Keywords: Law-Invariant Convex Risk Functional, Dual Representation, Robust Evaluation, Optimal Reinsurance Design, Budget Constraint

Suggested Citation

Liu, Fangda and Cai, Jun and Lemieux, Christiane and Wang, Ruodu, Convex Risk Functionals: Representation and Applications (July 9, 2018). Available at SSRN: https://ssrn.com/abstract=3216336 or http://dx.doi.org/10.2139/ssrn.3216336

Fangda Liu (Contact Author)

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

Waterloo, Ontario N2L 3G1
Canada

Jun Cai

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

Waterloo, Ontario N2L 3G1
Canada

Christiane Lemieux

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

Waterloo, Ontario N2L 3G1
Canada

Ruodu Wang

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

Waterloo, Ontario N2L 3G1
Canada

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