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Robust return risk measures
Robust return risk measures
- 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.
- Subjects :
- Statistics and Probability
Mathematical optimization
media_common.quotation_subject
Positive homogeneity
Characterization (mathematics)
01 natural sciences
010104 statistics & probability
Shortfall risk
Monetary value
0502 economics and business
Robustne
0101 mathematics
Invariant (mathematics)
Axiom
050205 econometrics
media_common
Mathematics
Orlicz norms and space
Mathematical finance
05 social sciences
Contrast (statistics)
Probability and statistics
Ambiguity
Dual (category theory)
Ambiguity averse preference
Expected shortfall
Convex risk measure
Time consistency
Statistics, Probability and Uncertainty
Mathematical economics
Orlicz premium
Finance
Subjects
Details
- Language :
- English
- ISSN :
- 18629679
- Volume :
- 12
- Issue :
- 1
- Database :
- OpenAIRE
- Journal :
- Mathematics and Financial Economics
- Accession number :
- edsair.doi.dedup.....4a6bd5d4a3e620411264a022eed3bb4c