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Optimization of Risk Measures

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Author Info
Andrzej Ruszczynski (Rutgers University)
Alexander Shapiro (Georgia Institute of Technology)

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Abstract

We consider optimization problems involving coherent risk measures. We derive necessary and sufficient conditions of optimality for these problems, and we discuss the nature of the nonanticipativity constraints. Next, we introdice dynamic risk measures, and we formulate multistage optimization problems involving these measures. Conditions similar to dynamic programming equations are developed. The theoretical considerations are illustrated with many examples of mean-risk models applied in practice.

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File URL: http://129.3.20.41/eps/ri/papers/0407/0407002.pdf
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Publisher Info
Paper provided by EconWPA in its series Risk and Insurance with number 0407002.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length: 40 pages
Date of creation: 24 Jul 2004
Date of revision:
Handle: RePEc:wpa:wuwpri:0407002

Note: Type of Document - pdf; pages: 40
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Web page: http://129.3.20.41

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Related research
Keywords: risk measures; mean-risk models; duality; optimization; dynamic programming;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Conditional Risk Mappings," Risk and Insurance 0404002, EconWPA, revised 08 Oct 2005. [Downloadable!]
  2. Frank Riedel, 2003. "Dynamic Coherent Risk Measures," Working Papers 03004, Stanford University, Department of Economics. [Downloadable!]
  3. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Convex Risk Functions," Risk and Insurance 0404001, EconWPA, revised 08 Oct 2005. [Downloadable!]
  4. Ogryczak, Wlodzimierz & Ruszczynski, Andrzej, 1999. "From stochastic dominance to mean-risk models: Semideviations as risk measures," European Journal of Operational Research, Elsevier, vol. 116(1), pages 33-50, July. [Downloadable!] (restricted)
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  5. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July. [Downloadable!] (restricted)
  6. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447. [Downloadable!] (restricted)
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