Convex measures of risk and trading constraints
- Cite this article as:
- Föllmer, H. & Schied, A. Finance Stochast (2002) 6: 429. doi:10.1007/s007800200072
We introduce the notion of a convex measure of risk, an extension of the concept of a coherent risk measure defined in Artzner et al. (1999), and we prove a corresponding extension of the representation theorem in terms of probability measures on the underlying space of scenarios. As a case study, we consider convex measures of risk defined in terms of a robust notion of bounded shortfall risk. In the context of a financial market model, it turns out that the representation theorem is closely related to the superhedging duality under convex constraints.