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Quasi-Logconvex Measures of Risk

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arxiv 2208.07694 v1 pith:LJHUMOCN submitted 2022-07-25 q-fin.RM math.PR

classification q-fin.RMmath.PR
keywords measuresriskquasi-logconvexclassgeneralizequasi-convexrepresentationacceptance
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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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  1. Generalized Orlicz premia

    q-fin.RM 2025-07 conditional novelty 7.0 of 10

    Generalized Orlicz premia with non-convex loss functions unify quantiles, expectiles, and L^p-quantiles, and cash-additivity characterizes them as L^p-quantiles.

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