IDEAS home Printed from
   My bibliography  Save this paper

Optimization of Risk Measures


  • Andrzej Ruszczynski

    (Rutgers University)

  • Alexander Shapiro

    (Georgia Institute of Technology)


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.

Suggested Citation

  • Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Risk Measures," Risk and Insurance 0407002, University Library of Munich, Germany.
  • Handle: RePEc:wpa:wuwpri:0407002
    Note: Type of Document - pdf; pages: 40

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 185-200, August.
    2. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Conditional Risk Mappings," Risk and Insurance 0404002, University Library of Munich, Germany, revised 08 Oct 2005.
    3. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Convex Risk Functions," Risk and Insurance 0404001, University Library of Munich, Germany, revised 08 Oct 2005.
    4. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    5. 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.
    6. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
    Full references (including those not matched with items on IDEAS)


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Borgonovo, E. & Peccati, L., 2011. "Finite change comparative statics for risk-coherent inventories," International Journal of Production Economics, Elsevier, vol. 131(1), pages 52-62, May.
    2. Eskandarzadeh, Saman & Eshghi, Kourosh, 2013. "Decision tree analysis for a risk averse decision maker: CVaR Criterion," European Journal of Operational Research, Elsevier, vol. 231(1), pages 131-140.
    3. Ban Kawas & Aurelie Thiele, 2017. "Log-robust portfolio management with parameter ambiguity," Computational Management Science, Springer, vol. 14(2), pages 229-256, April.
    4. Alexandre Street, 2010. "On the Conditional Value-at-Risk probability-dependent utility function," Theory and Decision, Springer, vol. 68(1), pages 49-68, February.
    5. Borgonovo, E. & Peccati, L., 2009. "Financial management in inventory problems: Risk averse vs risk neutral policies," International Journal of Production Economics, Elsevier, vol. 118(1), pages 233-242, March.
    6. Balbás, Alejandro & Balbás, Raquel & Mayoral, Silvia, 2009. "Portfolio choice and optimal hedging with general risk functions: A simplex-like algorithm," European Journal of Operational Research, Elsevier, vol. 192(2), pages 603-620, January.
    7. Giri, B.C., 2011. "Managing inventory with two suppliers under yield uncertainty and risk aversion," International Journal of Production Economics, Elsevier, vol. 133(1), pages 80-85, September.
    8. Birbil, S.I. & Frenk, J.B.G. & Kaynar, B. & N. Nilay, N., 2008. "Risk measures and their applications in asset management," Econometric Institute Research Papers EI 2008-14, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wpa:wuwpri:0407002. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.