Quasi-Logconvex Measures of Risk

TL;DR

This paper introduces quasi-logconvex risk measures, a new class that generalizes logconvex return risk measures, with dual representations, classification, and applications in portfolio choice and capital allocation.

Contribution

It fully characterizes quasi-logconvex risk measures, establishing their dual representation and providing a comprehensive taxonomy and applications.

Findings

Established dual representation of quasi-logconvex risk measures.

Provided classification and law-invariant representation.

Discussed applications in portfolio choice and capital allocation.

Abstract

This paper introduces and fully characterizes the novel class of quasi-logconvex measures of risk, to stand on equal footing with the rich class of quasi-convex measures of risk. Quasi-logconvex risk measures naturally generalize logconvex return risk measures, just like quasi-convex risk measures generalize convex monetary risk measures. We establish their dual representation and analyze their taxonomy in a few (sub)classification results. Furthermore, we characterize quasi-logconvex risk measures in terms of properties of families of acceptance sets and provide their law-invariant representation. Examples and applications to portfolio choice and capital allocation are also discussed.