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

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.
Scheda breve Scheda completa Scheda completa (DC)
Capitolo o saggio
dynamic
English
Risk measures for the 21st century
978-0-470-86154-7
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.
Frittelli, M; ROSAZZA GIANIN, E
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/5369
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