Entropy coherent and entropy convex measures of risk

We introduce two subclasses of convex measures of risk, referred to as entropy coherent and entropy convex measures of risk. Entropy coherent and entropy convex measures of risk are special cases of φ-coherent and φ-convex measures of risk. Contrary to the classical use of coherent and convex measures of risk, which for a given probabilistic model entails evaluating a financial position by considering its expected loss, φ-coherent and φ-convex measures of risk evaluate a financial position under a given probabilistic model by considering its normalized expected φ-loss. We prove that (i) entropy coherent and entropy convex measures of risk are obtained by requiring φ-coherent and φ-convex measures of risk to be translation invariant; (ii) convex, entropy convex, and entropy coherent measures of risk emerge as certainty equivalents under variational, homothetic, and multiple priors preferences upon requiring the certainty equivalents to be translation invariant; and (iii) φ-convex measures of risk are certainty equivalents under variational and homothetic preferences if and only if they are convex and entropy convex measures of risk. In addition, we study the properties of entropy coherent and entropy convex measures of risk, derive their dual conjugate function, and characterize entropy coherent and entropy convex measures of risk in terms of properties of the corresponding acceptance sets.

Netspar, Network for Studies on Pensions, Aging and Retirement, is a thinktank and knowledge network. Netspar is dedicated to promoting a wider understanding of the economic and social implications of pensions, aging and retirement in the Netherlands and Europe.

MORE ABOUT NETSPAR


Mission en strategy           •           Network           •           Organisation           •          Magazine
Board Brief            •            Actionplan 2023-2027           •           Researchagenda

ABOUT NETSPAR

Our partners

B20210618_Achmea_logo_grey
B20160708_universiteit utrecht
B20160708_erasmus
B20160708_ministeries
B20210909_SPMS_logo download greyscale smaller
View all partners