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Law invariant risk measures on L∞ (ℝd)

Author

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  • Ekeland Ivar

    (Université Paris-Dauphine, CEREMADE and Institut de Finance, Paris CEDEX 16, Frankreich)

  • Schachermayer Walter

Abstract

Kusuoka (2001) has obtained explicit representation theorems for comonotone risk measures and, more generally, for law invariant risk measures. These theorems pertain, like most of the previous literature, to the case of scalar-valued risks.Jouini, Meddeb, and Touzi (2004) and Burgert and Rüschendorf (2006) extended the notion of risk measures to the vector-valued case. Recently Ekeland, Galichon, and Henry (2009) and Rüschendorf (2006, 2010) obtained extensions of the above theorems of Kusuoka to this setting. Their results were confined to the regular case.In general, Kusuoka´s representation theorem for comonotone risk measures also involves a singular part. In the present work we give a full generalization of Kusuoka´s theorems to the vector-valued case. The singular component turns out to have a richer structure than in the scalar case.

Suggested Citation

  • Ekeland Ivar & Schachermayer Walter, 2011. "Law invariant risk measures on L∞ (ℝd)," Statistics & Risk Modeling, De Gruyter, vol. 28(3), pages 195-225, September.
    • Handle: RePEc:bpj:strimo:v:28:y:2011:i:3:p:195-225:n:3
    DOI: 10.1524/stnd.2011.1099
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    References listed on IDEAS

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