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Modeling portfolio efficiency using stochastic optimization with incomplete information and partial uncertainty

Author

Listed:
  • D. Torre

    (Université Côte d’Azur)

  • F. Mendivil

    (Acadia University)

  • M. Rocca

    (Universitá degli Studi dell’Insubria)

Abstract

Efficiency plays a crucial role in portfolio optimization. This notion is formulated by means of stochastic optimization techniques. Very often this problem is subject to partial uncertainty or incomplete information on the probability distribution and on the preferences expressed by means of the utility function. In this case both the objective function and the underlying probability measure are not known with precision. To address this kind of issues, we propose to model the notion of incomplete information by means of set-valued analysis and, therefore, we propose two different extensions of the classical model. In the first one we rely on the notion of set-valued function while the second one utilizes the notion of set-valued probability. For both of them we investigate stability properties. These results are also linked to the notion of robustness of the aforementioned problem. Finally we apply the obtained results to portfolio theory and stochastic dominance.

Suggested Citation

  • D. Torre & F. Mendivil & M. Rocca, 2024. "Modeling portfolio efficiency using stochastic optimization with incomplete information and partial uncertainty," Annals of Operations Research, Springer, vol. 334(1), pages 241-263, March.
    • Handle: RePEc:spr:annopr:v:334:y:2024:i:1:d:10.1007_s10479-021-04372-x
    DOI: 10.1007/s10479-021-04372-x
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    References listed on IDEAS

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    1. R. G. Vickson, 1975. "Stochastic Dominance Tests for Decreasing Absolute Risk Aversion. I. Discrete Random Variables," Management Science, INFORMS, vol. 21(12), pages 1438-1446, August.
    2. Ben Abdelaziz, Fouad & Masri, Hatem, 2010. "A compromise solution for the multiobjective stochastic linear programming under partial uncertainty," European Journal of Operational Research, Elsevier, vol. 202(1), pages 55-59, April.
    3. Davide La Torre & Franklin Mendivil, 2018. "Stochastic linear optimization under partial uncertainty and incomplete information using the notion of probability multimeasure," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 69(10), pages 1549-1556, October.
    4. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1931, October.
    5. Ben Abdelaziz, F. & Masri, H., 2005. "Stochastic programming with fuzzy linear partial information on probability distribution," European Journal of Operational Research, Elsevier, vol. 162(3), pages 619-629, May.
    6. Hiai, Fumio, 1978. "Radon-Nikodym theorems for set-valued measures," Journal of Multivariate Analysis, Elsevier, vol. 8(1), pages 96-118, March.
    7. Porter, R Burr & Gaumnitz, Jabk E, 1972. "Stochastic Dominance vs. Mean-Variance Portfolio Analysis: An Empirical Evaluation," American Economic Review, American Economic Association, vol. 62(3), pages 438-446, June.
    8. Oliver Linton & Thierry Post & Yoon‐Jae Whang, 2014. "Testing for the stochastic dominance efficiency of a given portfolio," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 59-74, June.
    9. Malavasi, Matteo & Ortobelli Lozza, Sergio & Trück, Stefan, 2021. "Second order of stochastic dominance efficiency vs mean variance efficiency," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1192-1206.
    10. Davide LA TORRE & Franklin MENDIVIL, 2007. "Iterated function systems on multifunctions and inverse problems," Departmental Working Papers 2007-32, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    11. R. G. Vickson, 1977. "Stochastic Dominance Tests for Decreasing Absolute Risk-Aversion II: General Random Variables," Management Science, INFORMS, vol. 23(5), pages 478-489, January.
    12. Fang, Yi & Post, Thierry, 2017. "Higher-degree stochastic dominance optimality and efficiency," European Journal of Operational Research, Elsevier, vol. 261(3), pages 984-993.
    13. repec:bla:jfinan:v:58:y:2003:i:5:p:1905-1932 is not listed on IDEAS
    14. D. La Torre & F. Mendivil, 2018. "Portfolio optimization under partial uncertainty and incomplete information: a probability multimeasure-based approach," Annals of Operations Research, Springer, vol. 267(1), pages 267-279, August.
    15. Levy, Haim, 1973. "Stochastic Dominance, Efficiency Criteria, and Efficient Portfolios: The Multi-Period Case," American Economic Review, American Economic Association, vol. 63(5), pages 986-994, December.
    16. Urli, Bruno & Nadeau, Raymond, 2004. "PROMISE/scenarios: An interactive method for multiobjective stochastic linear programming under partial uncertainty," European Journal of Operational Research, Elsevier, vol. 155(2), pages 361-372, June.
    17. Thierry Post & Valerio Potì, 2017. "Portfolio Analysis Using Stochastic Dominance, Relative Entropy, and Empirical Likelihood," Management Science, INFORMS, vol. 63(1), pages 153-165, January.
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