Geometrically convex return risk measures on AM-algebras (opens in new tab)

Monetary risk measures quantify the risk of uncertain monetary payoffs (or losses), whereas in time series analysis risk is typically assessed using logarithmic returns. Return risk measures (RRMs) provide an axiomatic foundation for this latter approach, which relies crucially on the positive cone of the space of essentially bounded random variables. We extend RRMs to general ordered vector spaces and characterize positive homogeneity via the g...