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Generalized Robust Optimization using the Notion of Set-Valued Probability.

Davide La Torre1, Franklin Mendivil2, Matteo Rocca3

  • 1SKEMA Business School, Université Côte d'Azur Sophia Antipolis Campus, Sophia Antipolis, France.

Journal of Optimization Theory and Applications
|September 2, 2025
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Summary
This summary is machine-generated.

This study introduces a robust framework using set-valued probabilities to estimate uncertain probabilities. It offers improved decision-making and resilience in financial modeling and risk management.

Keywords:
Portfolio OptimizationRisk MeasureRobustnessSet-Valued Probability Measure

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Area of Science:

  • Mathematical Statistics
  • Financial Mathematics
  • Decision Theory

Background:

  • Statistical estimation of probabilities is challenged by uncertainty and unknown values.
  • Existing methods may lack robustness when dealing with imprecise probabilistic information.

Purpose of the Study:

  • To propose a novel concept of robustness based on set-valued probabilities.
  • To provide a unified and versatile framework for statistical estimation under uncertainty.
  • To derive optimality, convexity, and stability conditions for enhanced robustness.

Main Methods:

  • Utilizing the framework of set-valued probabilities.
  • Employing scalarization techniques for set-valued probabilities.
  • Deriving optimality conditions and establishing generalized convexity and stability properties.

Main Results:

  • A novel, unified concept of robustness for probabilistic estimation.
  • Optimality, generalized convexity, and stability conditions derived from scalarization.
  • Demonstrated applicability in financial portfolio management and risk measure theory.

Conclusions:

  • The proposed set-valued probability framework offers a robust approach to statistical estimation.
  • The derived conditions enhance the reliability of probabilistic models in uncertain environments.
  • This framework provides powerful tools for optimizing decisions and ensuring resilience in finance and risk management.