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Dual Representations for Convex Risk Measures via Conjugate Duality

Author

Listed:
  • R. I. Boţ

    (Chemnitz University of Technology)

  • N. Lorenz

    (Chemnitz University of Technology)

  • G. Wanka

    (Chemnitz University of Technology)

Abstract

The aim of this paper is to give dual representations for different convex risk measures by employing their conjugate functions. To establish the formulas for the conjugates, we use on the one hand some classical results from convex analysis and on the other hand some tools from the conjugate duality theory. Some characterizations of so-called deviation measures recently given in the literature turn out to be direct consequences of our results.

Suggested Citation

  • R. I. Boţ & N. Lorenz & G. Wanka, 2010. "Dual Representations for Convex Risk Measures via Conjugate Duality," Journal of Optimization Theory and Applications, Springer, vol. 144(2), pages 185-203, February.
    • Handle: RePEc:spr:joptap:v:144:y:2010:i:2:d:10.1007_s10957-009-9595-3
    DOI: 10.1007/s10957-009-9595-3
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    References listed on IDEAS

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    1. R. Rockafellar & Stan Uryasev & Michael Zabarankin, 2006. "Generalized deviations in risk analysis," Finance and Stochastics, Springer, vol. 10(1), pages 51-74, January.
    2. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    3. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, Michael, 2006. "Master funds in portfolio analysis with general deviation measures," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 743-778, February.
    4. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
    5. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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    Cited by:

    1. Radu Boţ & Alina-Ramona Frătean, 2011. "Looking for appropriate qualification conditions for subdifferential formulae and dual representations for convex risk measures," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(2), pages 191-215, October.

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