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Solving optimal stopping problems under model uncertainty via empirical dual optimisation

Author

Listed:
  • Denis Belomestny

    (University of Duisburg–Essen
    National University Higher School of Economics)

  • Tobias Hübner

    (University of Duisburg–Essen)

  • Volker Krätschmer

    (University of Duisburg–Essen)

Abstract

In this work, we consider optimal stopping problems with model uncertainty incorporated into the formulation of the underlying objective function. Typically, the robust, efficient hedging of American options in incomplete markets may be described as optimal stopping of such kind. Based on a generalisation of the additive dual representation of Rogers (Math. Financ. 12:271–286, 2002) to the case of optimal stopping under model uncertainty, we develop a novel regression-based Monte Carlo algorithm for the approximation of the corresponding value function. The algorithm involves optimising a penalised empirical dual objective functional over a class of martingales. This formulation allows us to construct upper bounds for the optimal value with reduced complexity. Finally, we carry out a convergence analysis of the proposed algorithm and illustrate its performance by several numerical examples.

Suggested Citation

  • Denis Belomestny & Tobias Hübner & Volker Krätschmer, 2022. "Solving optimal stopping problems under model uncertainty via empirical dual optimisation," Finance and Stochastics, Springer, vol. 26(3), pages 461-503, July.
    • Handle: RePEc:spr:finsto:v:26:y:2022:i:3:d:10.1007_s00780-022-00480-z
    DOI: 10.1007/s00780-022-00480-z
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    References listed on IDEAS

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    More about this item

    Keywords

    Model uncertainty; Optimal stopping; Dual representation; Empirical dual optimisation; Generative models; Covering numbers; Concentration inequalities;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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