Robust Return Risk Measures

Mathematics and Financial Economics, pp. 1-28, 2017, DOI: 10.1007/s11579-017-0188-x

32 Pages Posted: 23 Aug 2016 Last revised: 13 Jun 2017

See all articles by Fabio Bellini

Fabio Bellini

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Roger J. A. Laeven

University of Amsterdam - Department of Quantitative Economics (KE)

Emanuela Rosazza Gianin

University of Milano-Bicocca - Dip. di Statistica e Metodi Quantitativi

Date Written: August 23, 2016

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 measures, thus paralleling the characterization in Weber (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 measures leads to several robustified versions of Orlicz risk measures and of their optimized translation invariant extensions (Rockafellar and Uryasev, 2000, Goovaerts et al., 2004), arising from an ambiguity averse approach as in Gilboa and Schmeidler (1989), Maccheroni et al. (2006), Chateauneuf and Faro (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.

Keywords: Orlicz premium, Shortfall risk, Robustness, Ambiguity averse preferences, Orlicz norms and spaces, Convex risk measures, Positive homogeneity

JEL Classification: D81, G10, G22

Suggested Citation

Bellini, Fabio and Laeven, Roger Jean Auguste and Rosazza Gianin, Emanuela, Robust Return Risk Measures (August 23, 2016). Mathematics and Financial Economics, pp. 1-28, 2017, DOI: 10.1007/s11579-017-0188-x. Available at SSRN: https://ssrn.com/abstract=2828181 or http://dx.doi.org/10.2139/ssrn.2828181

Fabio Bellini

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Milano, Milan
Italy

Roger Jean Auguste Laeven

University of Amsterdam - Department of Quantitative Economics (KE) ( email )

Valckenierstraat 65-67
Amsterdam, 1018 XE
Netherlands
+31 20 525 4252 (Phone)

HOME PAGE: http://www.rogerlaeven.com

Emanuela Rosazza Gianin (Contact Author)

University of Milano-Bicocca - Dip. di Statistica e Metodi Quantitativi ( email )

Milan
Italy

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