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Stochastic efficiency and inefficiency in portfolio optimization with incomplete information: a set-valued probability approach

Author

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  • D. La Torre

    (Université Côte d’Azur)

  • F. Mendivil

    (Acadia University)

Abstract

In this paper we extend the notion of stochastic efficiency and inefficiency in portfolio optimization to the case of incomplete information by means of set-valued probabilities. The notion of set-valued probability models the concept of incomplete information about the underlying probability space and the probability associated with each scenario. Unlike other approaches in literature, our notion of inefficiency is introduced by means of the Monge–Kantorovich metric. We provide some numerical examples to illustrate this approach.

Suggested Citation

  • D. La Torre & F. Mendivil, 2022. "Stochastic efficiency and inefficiency in portfolio optimization with incomplete information: a set-valued probability approach," Annals of Operations Research, Springer, vol. 311(2), pages 1085-1098, April.
    • Handle: RePEc:spr:annopr:v:311:y:2022:i:2:d:10.1007_s10479-020-03886-0
    DOI: 10.1007/s10479-020-03886-0
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    References listed on IDEAS

    as
    1. 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.
    2. repec:bla:jfinan:v:58:y:2003:i:5:p:1905-1932 is not listed on IDEAS
    3. 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.
    4. 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.
    5. Thierry Post, 2003. "Empirical Tests for Stochastic Dominance Efficiency," Journal of Finance, American Finance Association, vol. 58(5), pages 1905-1931, October.
    6. 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.
    7. F. Ben Abdelaziz & P. Lang & R. Nadeau, 1999. "Dominance and Efficiency in Multicriteria Decision under Uncertainty," Theory and Decision, Springer, vol. 47(3), pages 191-211, December.
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Xu, Peng, 2024. "Testing out-of-sample portfolio performance using second-order stochastic dominance constrained optimization approach," International Review of Financial Analysis, Elsevier, vol. 95(PA).

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