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Optimal stopping with signatures

Author

Listed:
  • Christian Bayer
  • Paul Hager
  • Sebastian Riedel
  • John Schoenmakers

Abstract

We propose a new method for solving optimal stopping problems (such as American option pricing in finance) under minimal assumptions on the underlying stochastic process $X$. We consider classic and randomized stopping times represented by linear and non-linear functionals of the rough path signature $\mathbb{X}^{

Suggested Citation

  • Christian Bayer & Paul Hager & Sebastian Riedel & John Schoenmakers, 2021. "Optimal stopping with signatures," Papers 2105.00778, arXiv.org.
    • Handle: RePEc:arx:papers:2105.00778
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    File URL: http://arxiv.org/pdf/2105.00778
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    References listed on IDEAS

    as
    1. Christian Bayer & Fabian Andsem Harang & Paolo Pigato, 2020. "Log-modulated rough stochastic volatility models," Papers 2008.03204, arXiv.org, revised May 2021.
    2. Bennedsen, Mikkel, 2017. "A rough multi-factor model of electricity spot prices," Energy Economics, Elsevier, vol. 63(C), pages 301-313.
    3. Christian Bayer & Raúl Tempone & Sören Wolfers, 2020. "Pricing American options by exercise rate optimization," Quantitative Finance, Taylor & Francis Journals, vol. 20(11), pages 1749-1760, November.
    4. Bruno Dupire, 2019. "Functional Itô calculus," Quantitative Finance, Taylor & Francis Journals, vol. 19(5), pages 721-729, May.
    5. Mikkel Bennedsen, 2020. "Semiparametric estimation and inference on the fractal index of Gaussian and conditionally Gaussian time series data," Econometric Reviews, Taylor & Francis Journals, vol. 39(9), pages 875-903, October.
    6. Eyal Neuman & Mathieu Rosenbaum, 2017. "Fractional Brownian motion with zero Hurst parameter: a rough volatility viewpoint," Papers 1711.00427, arXiv.org, revised May 2018.
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    Cited by:

    1. Boming Ning & Prakash Chakraborty & Kiseop Lee, 2023. "Optimal Entry and Exit with Signature in Statistical Arbitrage," Papers 2309.16008, arXiv.org, revised Mar 2024.
    2. Christa Cuchiero & Francesca Primavera & Sara Svaluto-Ferro, 2022. "Universal approximation theorems for continuous functions of c\`adl\`ag paths and L\'evy-type signature models," Papers 2208.02293, arXiv.org, revised Aug 2023.
    3. Christa Cuchiero & Guido Gazzani & Sara Svaluto-Ferro, 2022. "Signature-based models: theory and calibration," Papers 2207.13136, arXiv.org.
    4. Christa Cuchiero & Philipp Schmocker & Josef Teichmann, 2023. "Global universal approximation of functional input maps on weighted spaces," Papers 2306.03303, arXiv.org, revised Feb 2024.
    5. Christa Cuchiero & Guido Gazzani & Janka Moller & Sara Svaluto-Ferro, 2023. "Joint calibration to SPX and VIX options with signature-based models," Papers 2301.13235, arXiv.org.
    6. Christa Cuchiero & Janka Moller, 2023. "Signature Methods in Stochastic Portfolio Theory," Papers 2310.02322, arXiv.org, revised Mar 2024.
    7. Christa Cuchiero & Sara Svaluto-Ferro & Josef Teichmann, 2023. "Signature SDEs from an affine and polynomial perspective," Papers 2302.01362, arXiv.org.

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