Back to Search Start Over

Robust return risk measures

Robust return risk measures

Authors :
E. Rosazza Gianin
Roger J. A. Laeven
Fabio Bellini
Faculteit Economie en Bedrijfskunde
Actuarial Science & Mathematical Finance (ASE, FEB)
Bellini, F
Laeven, R
Rosazza Gianin, E
Source :
Mathematics and Financial Economics, 12(1), 5-32. Springer Verlag
Publication Year :
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 Follmer 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.

Details

Language :
English
ISSN :
18629679
Volume :
12
Issue :
1
Database :
OpenAIRE
Journal :
Mathematics and Financial Economics
Accession number :
edsair.doi.dedup.....4a6bd5d4a3e620411264a022eed3bb4c