Primal and dual optimal stopping with signatures
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910817716273152 |
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| author | Bayer, Christian Pelizzari, Luca Schoenmakers, John |
| author_facet | Bayer, Christian Pelizzari, Luca Schoenmakers, John |
| contents | 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 $L^p-$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 famous 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_03444 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Primal and dual optimal stopping with signatures Bayer, Christian Pelizzari, Luca Schoenmakers, John Mathematical Finance Probability 60L10, 60L20, 91G20, 91G60 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 $L^p-$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 famous 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. |
| title | Primal and dual optimal stopping with signatures |
| topic | Mathematical Finance Probability 60L10, 60L20, 91G20, 91G60 |
| url | https://arxiv.org/abs/2312.03444 |