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.
Frittelli, M., ROSAZZA GIANIN, E. (2004). Dynamic convex risk measures. In G. Szegö (a cura di), Risk measures for the 21st century (pp. 227-248). John Wiley and Sons Ltd.
Dynamic convex risk measures
ROSAZZA GIANIN, EMANUELA
2004
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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