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Two-stage portfolio optimization with higher-order conditional measures of risk


  • Sıtkı Gülten


  • Andrzej Ruszczyński



We describe a study of application of novel risk modeling and optimization techniques to daily portfolio management. In the first part of the study, we develop and compare specialized methods for scenario generation and scenario tree construction. In the second part, we construct a two-stage stochastic programming problem with conditional measures of risk, which is used to re-balance the portfolio on a rolling horizon basis, with transaction costs included in the model. In the third part, we present an extensive simulation study on real-world data of several versions of the methodology. We show that two-stage models outperform single-stage models in terms of long-term performance. We also show that using high-order risk measures is superior to first-order measures. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • Sıtkı Gülten & Andrzej Ruszczyński, 2015. "Two-stage portfolio optimization with higher-order conditional measures of risk," Annals of Operations Research, Springer, vol. 229(1), pages 409-427, June.
  • Handle: RePEc:spr:annopr:v:229:y:2015:i:1:p:409-427:10.1007/s10479-014-1768-2
    DOI: 10.1007/s10479-014-1768-2

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    References listed on IDEAS

    1. Marco Frittelli & Giacomo Scandolo, 2006. "Risk Measures And Capital Requirements For Processes," Mathematical Finance, Wiley Blackwell, vol. 16(4), pages 589-612, October.
    2. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Conditional Risk Mappings," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 544-561, August.
    3. Matmoura, Yassine & Penev, Spiridon, 2013. "Multistage optimization of option portfolio using higher order coherent risk measures," European Journal of Operational Research, Elsevier, vol. 227(1), pages 190-198.
    4. Andrzej Ruszczyński & Alexander Shapiro, 2006. "Optimization of Convex Risk Functions," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 433-452, August.
    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.
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    7. Georg Ch Pflug & Werner Römisch, 2007. "Modeling, Measuring and Managing Risk," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 6478, October.
    8. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
    9. Ronald Hochreiter & Georg Pflug, 2007. "Financial scenario generation for stochastic multi-stage decision processes as facility location problems," Annals of Operations Research, Springer, vol. 152(1), pages 257-272, July.
    10. 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.
    11. Naomi Miller & Andrzej Ruszczyński, 2011. "Risk-Averse Two-Stage Stochastic Linear Programming: Modeling and Decomposition," Operations Research, INFORMS, vol. 59(1), pages 125-132, February.
    12. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
    13. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath & Hyejin Ku, 2007. "Coherent multiperiod risk adjusted values and Bellman’s principle," Annals of Operations Research, Springer, vol. 152(1), pages 5-22, July.
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