Primal and dual optimal stopping with signatures
Authors
- Bayer, Christian
ORCID: 0000-0002-9116-0039 - Pelizzari, Luca
- Schoenmakers, John G. M.
ORCID: 0000-0002-4389-8266
2020 Mathematics Subject Classification
- 60L10 60L20 91G20
Keywords
- Signature, optimal stopping, rough paths, Monte Carlo, rough volatility
DOI
Abstract
We propose two signature-based methods to solve the optimal stopping problem - that is, to price American options - in non-Markovian frameworks. Both methods rely on a global approximation result for Lp-functionals on rough path-spaces, using linear functionals of robust, rough path signatures. In the primal formulation, we present a non-Markovian generalization of the fa- mous Longstaff--Schwartz algorithm, using linear functionals of the signature as regression basis. For the dual formulation, we parametrize 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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