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Tractable Almost Stochastic Dominance

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  • Lizyayev, Andrey
  • Ruszczyński, Andrzej

Abstract

LL-Almost Stochastic Dominance (LL-ASD) is a relaxation of the Stochastic Dominance (SD) concept proposed by Leshno and Levy that explains more of realistic preferences observed in practice than SD alone does. Unfortunately, numerical applications of this concept, such as identifying if a given portfolio is efficient or determining a marketed portfolio that dominates a given benchmark, are computationally prohibitive due to the structure of LL-ASD. We propose a new Almost Stochastic Dominance (ASD) concept that is computationally tractable. For instance, a marketed dominating portfolio can be identified by solving a simple linear programming problem. Moreover, the new concept performs well on all the intuitive examples from the literature, and in some cases leads to more realistic predictions than the earlier concept. We develop some properties of ASD, formulate efficient optimization models, and apply the concept to analyzing investors’ preferences between bonds and stocks for the long run.

Suggested Citation

  • Lizyayev, Andrey & Ruszczyński, Andrzej, 2012. "Tractable Almost Stochastic Dominance," European Journal of Operational Research, Elsevier, vol. 218(2), pages 448-455.
  • Handle: RePEc:eee:ejores:v:218:y:2012:i:2:p:448-455
    DOI: 10.1016/j.ejor.2011.11.019
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    Cited by:

    1. Topaloglou, Nikolas & Tsionas, Mike G., 2020. "Stochastic dominance tests," Journal of Economic Dynamics and Control, Elsevier, vol. 112(C).
    2. Christodoulakis, George & Mohamed, Abdulkadir & Topaloglou, Nikolas, 2018. "Optimal privatization portfolios in the presence of arbitrary risk aversion," European Journal of Operational Research, Elsevier, vol. 265(3), pages 1172-1191.
    3. Zagst, Rudi & Kraus, Julia & Bertrand, Philippe, 2019. "Option-Based performance participation," Journal of Banking & Finance, Elsevier, vol. 105(C), pages 44-61.
    4. Michel Denuit & Rachel Huang & Larry Tzeng, 2014. "Bivariate almost stochastic dominance," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 57(2), pages 377-405, October.
    5. 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.
    6. William B. Haskell & Alejandro Toriello, 2018. "Modeling Stochastic Dominance as Infinite-Dimensional Constraint Systems via the Strassen Theorem," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 726-742, September.
    7. Denuit, Michel M. & Huang, Rachel J. & Tzeng, Larry Y. & Wang, Christine W., 2014. "Almost marginal conditional stochastic dominance," Journal of Banking & Finance, Elsevier, vol. 41(C), pages 57-66.
    8. Ruchika Sehgal & Aparna Mehra, 2019. "Enhanced indexing using weighted conditional value at risk," Annals of Operations Research, Springer, vol. 280(1), pages 211-240, September.
    9. Fang, Yi & Post, Thierry, 2017. "Higher-degree stochastic dominance optimality and efficiency," European Journal of Operational Research, Elsevier, vol. 261(3), pages 984-993.
    10. Ng, Pin & Wong, Wing-Keung & Xiao, Zhijie, 2017. "Stochastic dominance via quantile regression with applications to investigate arbitrage opportunity and market efficiency," European Journal of Operational Research, Elsevier, vol. 261(2), pages 666-678.
    11. William B. Haskell & J. George Shanthikumar & Z. Max Shen, 2017. "Aspects of optimization with stochastic dominance," Annals of Operations Research, Springer, vol. 253(1), pages 247-273, June.
    12. Post, Thierry & Kopa, Miloš, 2013. "General linear formulations of stochastic dominance criteria," European Journal of Operational Research, Elsevier, vol. 230(2), pages 321-332.
    13. Pinar, Mehmet & Stengos, Thanasis & Topaloglou, Nikolas, 2020. "On the construction of a feasible range of multidimensional poverty under benchmark weight uncertainty," European Journal of Operational Research, Elsevier, vol. 281(2), pages 415-427.
    14. Dupačová, Jitka & Kopa, Miloš, 2014. "Robustness of optimal portfolios under risk and stochastic dominance constraints," European Journal of Operational Research, Elsevier, vol. 234(2), pages 434-441.
    15. 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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