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Optimization of Risk Measures

Author

Listed:
  • Andrzej Ruszczynski

    (Rutgers University)

  • Alexander Shapiro

    (Georgia Institute of Technology)

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.

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
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/ri/papers/0407/0407002.pdf
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    References listed on IDEAS

    as
    1. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Conditional Risk Mappings," Risk and Insurance 0404002, University Library of Munich, Germany, revised 08 Oct 2005.
    2. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Convex Risk Functions," Risk and Insurance 0404001, University Library of Munich, Germany, revised 08 Oct 2005.
    3. 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.
    4. Riedel, Frank, 2004. "Dynamic coherent risk measures," Stochastic Processes and their Applications, Elsevier, vol. 112(2), pages 185-200, August.
    5. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, 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

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    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.

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