On σ−additive robust representation of convex risk measures for unbounded financial positions in the presence of uncertainty about the market model

Abstract

Recently, Frittelli and Scandolo extend the notion of risk measures, originally introduced by Artzner, Delbaen, Eber and Heath, to the risk assessment of abstract financial positions, including pay offs spread over different dates, where liquid derivatives are admitted to serve as financial instruments. The paper deals with σ−additive robust representations of convex risk measures in the extended sense, dropping the assumption of an existing market model, and allowing also unbounded financial positions. The results may be applied for the case that a market model is available, and they encompass as well as improve criteria obtained for robust representations of the original convex risk measures for bounded positions.