Convex risk functionals: Representation and applications

Fangda Liu, Jun Cai, Christiane Lemieux and Ruodu Wang

Insurance: Mathematics and Economics, 2020, vol. 90, issue C, 66-79

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 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (19)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:90:y:2020:i:c:p:66-79

DOI: 10.1016/j.insmatheco.2019.10.007

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