Convex measures of risk and trading constraints

TL;DR: In this paper, the authors 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 prove a corresponding extension of representation theorem in terms of probability measures on the underlying space of scenarios.

Abstract: 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.

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Frequently asked questions

Q1. What are the contributions in this paper?

In this paper, the authors discuss the importance of human-human interaction in the context of cyber bullying.