Solving optimal stopping problems under model uncertainty via empirical dual optimisation

Denis Belomestny (), Tobias Hübner () and Volker Krätschmer ()
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Denis Belomestny: University of Duisburg–Essen
Tobias Hübner: University of Duisburg–Essen
Volker Krätschmer: University of Duisburg–Essen

Finance and Stochastics, 2022, vol. 26, issue 3, No 3, 503 pages

Abstract: 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.

Keywords: Model uncertainty; Optimal stopping; Dual representation; Empirical dual optimisation; Generative models; Covering numbers; Concentration inequalities; 60G40; 90C47; 91G20; 60G17 (search for similar items in EconPapers)
JEL-codes: C73 D81 G12 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00780-022-00480-z

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