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Generalized Robust Optimization using the Notion of Set-Valued Probability

Author

Listed:
  • Davide La Torre

    (Université Côte d’Azur Sophia Antipolis Campus)

  • Franklin Mendivil

    (Acadia University)

  • Matteo Rocca

    (Universitá degli Studi dell’Insubria)

Abstract

We propose a novel concept of robustness grounded in the framework of set-valued probabilities, offering a unified and versatile approach to tackling challenges associated with the statistical estimation of uncertain or unknown probabilities. By employing scalarization techniques for set-valued probabilities, we derive optimality conditions. Additionally, we establish generalized convexity properties and stability conditions, which further underpin the robustness of our approach. This comprehensive framework finds significant applications in areas such as financial portfolio management and risk measure theory, where it provides powerful tools for addressing uncertainty, optimizing decision-making, and ensuring resilience against variability in probabilistic models.

Suggested Citation

  • Davide La Torre & Franklin Mendivil & Matteo Rocca, 2025. "Generalized Robust Optimization using the Notion of Set-Valued Probability," Journal of Optimization Theory and Applications, Springer, vol. 207(3), pages 1-26, December.
    • Handle: RePEc:spr:joptap:v:207:y:2025:i:3:d:10.1007_s10957-025-02790-6
    DOI: 10.1007/s10957-025-02790-6
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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    5. Elyés Jouini & Moncef Meddeb & Nizar Touzi, 2004. "Vector-valued coherent risk measures," Finance and Stochastics, Springer, vol. 8(4), pages 531-552, November.
    6. 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.
    7. 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.
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    9. repec:dau:papers:123456789/353 is not listed on IDEAS
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