In this paper we provide an axiomatic foundation to Orlicz risk measures in terms of properties of their acceptance sets, by exploiting their natural correspondence with shortfall risk Föllmer and Schied (Stochastic finance. De Gruyter, Berlin, 2011), thus paralleling the characterization in Weber (Math Financ 16:419–442, 2006). From a financial point of view, Orlicz risk measures assess the stochastic nature of returns, in contrast to the common use of risk measures to assess the stochastic nature of a position’s monetary value. The correspondence with shortfall risk leads to several robustified versions of Orlicz risk measures, and of their optimized translation invariant extensions (Rockafellar and Uryasev in J Risk 2:21–42, 2000, Goovaerts et al. in Insur Math Econ 34:505–516, 2004), arising from an ambiguity averse approach as in Gilboa and Schmeidler (J Math Econ 18:141–153, 1989), Maccheroni et al. (Econometrica 74:1447–1498, 2006), Chateauneuf and Faro (J Math Econ 45:535–558, 2010), or from a multiplicity of Young functions. We study the properties of these robust Orlicz risk measures, derive their dual representations, and provide some examples and applications.

Bellini, F., Laeven, R., Rosazza Gianin, E. (2018). Robust return risk measures. MATHEMATICS AND FINANCIAL ECONOMICS, 12(1), 5-32 [10.1007/s11579-017-0188-x].

Robust return risk measures

Bellini, F;Rosazza Gianin, E
2018

Abstract

In this paper we provide an axiomatic foundation to Orlicz risk measures in terms of properties of their acceptance sets, by exploiting their natural correspondence with shortfall risk Föllmer and Schied (Stochastic finance. De Gruyter, Berlin, 2011), thus paralleling the characterization in Weber (Math Financ 16:419–442, 2006). From a financial point of view, Orlicz risk measures assess the stochastic nature of returns, in contrast to the common use of risk measures to assess the stochastic nature of a position’s monetary value. The correspondence with shortfall risk leads to several robustified versions of Orlicz risk measures, and of their optimized translation invariant extensions (Rockafellar and Uryasev in J Risk 2:21–42, 2000, Goovaerts et al. in Insur Math Econ 34:505–516, 2004), arising from an ambiguity averse approach as in Gilboa and Schmeidler (J Math Econ 18:141–153, 1989), Maccheroni et al. (Econometrica 74:1447–1498, 2006), Chateauneuf and Faro (J Math Econ 45:535–558, 2010), or from a multiplicity of Young functions. We study the properties of these robust Orlicz risk measures, derive their dual representations, and provide some examples and applications.
Articolo in rivista - Articolo scientifico
Ambiguity averse preferences; Convex risk measures; Orlicz norms and spaces; Orlicz premium; Positive homogeneity; Robustness; Shortfall risk;
Ambiguity averse preferences; Convex risk measures; Orlicz norms and spaces; Orlicz premium; Positive homogeneity; Robustness; Shortfall risk; Statistics and Probability; Finance; Statistics, Probability and Uncertainty
English
2018
12
1
5
32
partially_open
Bellini, F., Laeven, R., Rosazza Gianin, E. (2018). Robust return risk measures. MATHEMATICS AND FINANCIAL ECONOMICS, 12(1), 5-32 [10.1007/s11579-017-0188-x].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/182827
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