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Solving Optimal Stopping Problems via Randomization and Empirical Dual Optimization

Author

Listed:
  • Denis Belomestny

    (Department of Mathematics, University of Duisburg-Essen, 47057 Duisburg, Germany)

  • Christian Bender

    (Department of Mathematics, Saarland University, 66123 Saarbrücken, Germany)

  • John Schoenmakers

    (Weierstrass Institute for Applied Analysis and Stochastics, 10117 Berlin, Germany)

Abstract

In this paper, we consider optimal stopping problems in their dual form. In this way, the optimal stopping problem can be reformulated as a problem of stochastic average approximation (SAA) that can be solved via linear programming. By randomizing the initial value of the underlying process, we enforce solutions with zero variance while preserving the linear programming structure of the problem. A careful analysis of the randomized SAA algorithm shows that it enjoys favorable properties such as faster convergence rates and reduced complexity compared with the nonrandomized procedure. We illustrate the performance of our algorithm on several benchmark examples.

Suggested Citation

  • Denis Belomestny & Christian Bender & John Schoenmakers, 2023. "Solving Optimal Stopping Problems via Randomization and Empirical Dual Optimization," Mathematics of Operations Research, INFORMS, vol. 48(3), pages 1454-1480, August.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:3:p:1454-1480
    DOI: 10.1287/moor.2022.1306
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