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Dual Representations for Convex Risk Measures via Conjugate Duality

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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.

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Authors and Affiliations

  1. Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany

    R. I. Boţ, N. Lorenz & G. Wanka

Authors
  1. R. I. Boţ
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  2. N. Lorenz
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  3. G. Wanka
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Corresponding author

Correspondence to G. Wanka.

Additional information

Communicated by X.Q. Yang.

The research of R.I. Boţ and G. Wanka was partially supported by DFG (German Research Foundation), Project WA 922/1-3.

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Boţ, R.I., Lorenz, N. & Wanka, G. Dual Representations for Convex Risk Measures via Conjugate Duality. J Optim Theory Appl 144, 185–203 (2010). https://doi.org/10.1007/s10957-009-9595-3

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  • DOI: https://doi.org/10.1007/s10957-009-9595-3

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