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Primal and dual optimal stopping with signatures

Christian Bayer et al.

Finance and Stochastics2025https://doi.org/10.1007/s00780-025-00570-8article
AJG 3ABDC A
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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.

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https://doi.org/https://doi.org/10.1007/s00780-025-00570-8

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@article{christian2025,
  title        = {{Primal and dual optimal stopping with signatures}},
  author       = {Christian Bayer et al.},
  journal      = {Finance and Stochastics},
  year         = {2025},
  doi          = {https://doi.org/https://doi.org/10.1007/s00780-025-00570-8},
}

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Primal and dual optimal stopping with signatures

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0.50

Balanced mode · F 0.40 / M 0.15 / V 0.05 / R 0.40

F · citation impact0.50 × 0.4 = 0.20
M · momentum0.50 × 0.15 = 0.07
V · venue signal0.50 × 0.05 = 0.03
R · text relevance †0.50 × 0.4 = 0.20

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