We introduce the notion of a convex measure of risk, an extension of the concept of a coherent risk measure defined in … the underlying space of scenarios. As a case study, we consider convex measures of risk defined in terms of a robust not … ion of bounded shortfall risk. In the context of a financial market model, it turns out that the representation theorem is …

In Lecesne and Roncoroni (2013), we introduce the notion of monetary measure of risk borne by any financial claim. Our … presentation moves from general definitions to concrete instances, including the benchmark measure Value-at-Risk (VaR). Part II … develops a treatment of the class of coherent (monetary) measures of risk put forward by Artzner et al. (1999). Our goal is to …