Quasi-Logconvex Measures of Risk
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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.
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Geometrically convex return risk measures on AM-algebras
Extends return risk measures to AM-algebras, introducing systemic and vector-valued RRMs with finiteness, continuity, and dual/aggregation representations.
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