Abstract
Aumann and Serrano (J Political Econ 116(5):810–836, 2008) introduce the axiom of duality, which ensures that risk measures respect comparative risk aversion. This paper characterizes all dual risk measures by a simple equivalent condition. This equivalence provides a decomposition result and a construction method, which is used to analyze concrete dual measures. Moreover, this paper aims to extend this characterization to the most general setting. Compared with Aumann and Serrano (2008), it, therefore, relaxes the axiom of positive homogeneity, and allows for risk-neutral and risk-seeking agents, as well as for all integrable gambles.
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Notes
We exclude the trivial case of gambles, which equal \(0\) almost surely, for the clarity of presentation throughout the paper. This exclusion is no restriction in our context of decision-making, as the zero-gambles does not affect expected utility.
Aumann and Serrano (2008) further suggest an extension to Case \(A\) and to a variation of Case \(R\) without providing mathematical proofs.
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Acknowledgments
The author thanks the two anonymous referees, Damir Filipović, Eva Lüktebohmert-Holtz, Traian Pirvu, Frank Riedel, and numerous seminar participants for many helpful comments and discussions. The views expressed in this article are the author’s personal opinions and do not necessarily reflect the views of the Deutsche Bundesbank or its staff. This study is supported by the National Centre of Competence in Research “Financial Valuation and Risk Management” (NCCR FINRISK).
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Schulze, K. General dual measures of riskiness. Theory Decis 78, 289–304 (2015). https://doi.org/10.1007/s11238-014-9421-8
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DOI: https://doi.org/10.1007/s11238-014-9421-8