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Frontiers of Stochastically Nondominated Portfolios

Author

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  • Andrzej Ruszczynski
  • Robert J. Vanderbei

Abstract

We consider the problem of constructing a portfolio of finitely many assets whose returns are described by a discrete joint distribution.We propose mean-risk models that are solvable by linear programming and generate portfolios whose returns are nondominated in the sense of second-order stochastic dominance. Next, we develop a specialized parametric method for recovering the entire mean-risk efficient frontiers of these models and we illustrate its operation on a large data set involving thousands of assets and realizations. Copyright The Econometric Society 2003.

Suggested Citation

  • Andrzej Ruszczynski & Robert J. Vanderbei, 2003. "Frontiers of Stochastically Nondominated Portfolios," Econometrica, Econometric Society, vol. 71(4), pages 1287-1297, July.
    • Handle: RePEc:ecm:emetrp:v:71:y:2003:i:4:p:1287-1297
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    Cited by:

    1. Xue, Jing-Hao & Titterington, D. Michael, 2011. "The p-folded cumulative distribution function and the mean absolute deviation from the p-quantile," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1179-1182, August.
    2. Hirschberger, Markus & Qi, Yue & Steuer, Ralph E., 2010. "Large-scale MV efficient frontier computation via a procedure of parametric quadratic programming," European Journal of Operational Research, Elsevier, vol. 204(3), pages 581-588, August.
    3. Andrey Lizyayev, 2012. "Stochastic dominance efficiency analysis of diversified portfolios: classification, comparison and refinements," Annals of Operations Research, Springer, vol. 196(1), pages 391-410, July.
    4. Li, Xiaoming, 2008. "Demand evolution in stochastic inventory systems: Riskiness increase," International Journal of Production Economics, Elsevier, vol. 116(2), pages 182-189, December.
    5. Gilbert W. Bassett, 2004. "Pessimistic Portfolio Allocation and Choquet Expected Utility," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 477-492.
    6. Manganelli, Simone, 2007. "Asset allocation by penalized least squares," Working Paper Series 723, European Central Bank.
    7. Jitka Dupačová & Miloš Kopa, 2012. "Robustness in stochastic programs with risk constraints," Annals of Operations Research, Springer, vol. 200(1), pages 55-74, November.
    8. Tara Rengarajan & Nedialko Dimitrov & David P. Morton, 2013. "Convex Approximations of a Probabilistic Bicriteria Model with Disruptions," INFORMS Journal on Computing, INFORMS, vol. 25(1), pages 147-160, February.
    9. Lizyayev, Andrey & Ruszczyński, Andrzej, 2012. "Tractable Almost Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 218(2), pages 448-455.
    10. Lozano, Sebastián & Gutiérrez, Ester, 2008. "Data envelopment analysis of mutual funds based on second-order stochastic dominance," European Journal of Operational Research, Elsevier, vol. 189(1), pages 230-244, August.
    11. Nasim Dehghan Hardoroudi & Abolfazl Keshvari & Markku Kallio & Pekka Korhonen, 2017. "Solving cardinality constrained mean-variance portfolio problems via MILP," Annals of Operations Research, Springer, vol. 254(1), pages 47-59, July.
    12. Maskooki, Alaleh & Kallio, Markku, 2023. "A bi-criteria moving-target travelling salesman problem under uncertainty," European Journal of Operational Research, Elsevier, vol. 309(1), pages 271-285.
    13. Kallio, Markku & Dehghan Hardoroudi, Nasim, 2019. "Advancements in stochastic dominance efficiency tests," European Journal of Operational Research, Elsevier, vol. 276(2), pages 790-794.
    14. Dentcheva, Darinka & Ruszczynski, Andrzej, 2006. "Portfolio optimization with stochastic dominance constraints," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 433-451, February.
    15. Victor Lebreton, 2007. "Le trading algorithmique," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00332823, HAL.
    16. 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.
    17. Bruni, Renato & Cesarone, Francesco & Scozzari, Andrea & Tardella, Fabio, 2017. "On exact and approximate stochastic dominance strategies for portfolio selection," European Journal of Operational Research, Elsevier, vol. 259(1), pages 322-329.
    18. Rustam Ibragimov, 2004. "Shifting paradigms: on the robustness of economic models to heavy-tailedness assumptions," Econometric Society 2004 Latin American Meetings 105, Econometric Society.
    19. Felix Fie{ss}inger & Mitja Stadje, 2023. "Time-Consistent Asset Allocation for Risk Measures in a L\'evy Market," Papers 2305.09471, arXiv.org, revised Jun 2023.
    20. Heufer, Jan, 2014. "Nonparametric comparative revealed risk aversion," Journal of Economic Theory, Elsevier, vol. 153(C), pages 569-616.
    21. Sungyong Choi & Andrzej Ruszczyński & Yao Zhao, 2011. "A Multiproduct Risk-Averse Newsvendor with Law-Invariant Coherent Measures of Risk," Operations Research, INFORMS, vol. 59(2), pages 346-364, April.
    22. Haim Shalit & Shlomo Yitzhaki, 2010. "How does beta explain stochastic dominance efficiency?," Review of Quantitative Finance and Accounting, Springer, vol. 35(4), pages 431-444, November.
    23. Miller, Naomi & Ruszczynski, Andrzej, 2008. "Risk-adjusted probability measures in portfolio optimization with coherent measures of risk," European Journal of Operational Research, Elsevier, vol. 191(1), pages 193-206, November.
    24. Xi Yang & Jacek Gondzio & Andreas Grothey, 2010. "Asset liability management modelling with risk control by stochastic dominance," Journal of Asset Management, Palgrave Macmillan, vol. 11(2), pages 73-93, June.
    25. Kallio, Markku & Dehghan Hardoroudi, Nasim, 2018. "Second-order stochastic dominance constrained portfolio optimization: Theory and computational tests," European Journal of Operational Research, Elsevier, vol. 264(2), pages 675-685.

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