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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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Generalized Orlicz premia
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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