Primal and dual optimal stopping with signatures

Christian Bayer (), Luca Pelizzari () and John Schoenmakers ()
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Christian Bayer: Weierstrass Institut
Luca Pelizzari: Weierstrass Institut
John Schoenmakers: Weierstrass Institut

Finance and Stochastics, 2025, vol. 29, issue 4, No 2, 1014 pages

Abstract: Abstract We propose two signature-based methods to solve an optimal stopping problem – that is, to price American options – in non-Markovian frameworks. Both methods rely on a global approximation result for L p $L^{p}$ -functionals on rough-path spaces, using linear functionals of robust, rough-path signatures. In the primal formulation, we present a non-Markovian generalisation of the famous Longstaff–Schwartz algorithm, using linear functionals of the signature as regression basis. For the dual formulation, we parametrise the space of square-integrable martingales using linear functionals of the signature and apply a sample average approximation. We prove convergence for both methods and present first numerical examples in non-Markovian and non-semimartingale regimes.

Keywords: Signature; Optimal stopping; Rough paths; Monte Carlo; Rough volatility; 60L10; 60L20; 91G20; 91G60 (search for similar items in EconPapers)
JEL-codes: C63 G12 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00780-025-00570-8

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