Dynamic convex risk measures

Marco Frittelli · Emanuela Rosazza Gianin

136 citations0/0 files storedBOA (University of Milano-Bicocca)

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Stochastic processes and financial applications Risk and Portfolio Optimization Probability and Risk Models

Abstract

We provide a representation theorem for convex risk measures defined on $L^p(\Omega,\mathcal{F},P)$ spaces, $1\leq p \leq + \infty$, and we discuss the financial meaning of the convexity axiom. We characterize those convex risk measures that are law invariant and show the link between convex risk measures and utility based prices in incomplete market models. As a natural extension of the representation of convex risk measures, we introduce and study a class of dynamic risk measures.

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