We provide a representation theorem for convex risk measures defined on L^{p}(Ω,F,P) spaces, 1≤p≤+∞, 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 convex risk measures.
Dynamic convex risk measures / M. Frittelli, E. Rosazza Gianin - In: Risk measures for the 21th Century / [a cura di] Giorgio Szego. - New York : John Wiley & Sons, 2004. - ISBN 978-0-470-86154-7. - pp. 227-248
Dynamic convex risk measures
M. FrittelliPrimo
;
2004
Abstract
We provide a representation theorem for convex risk measures defined on L^{p}(Ω,F,P) spaces, 1≤p≤+∞, 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 convex risk measures.
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