{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/primal-and-dual-optimal-stopping-with","title":"Primal and dual optimal stopping with signatures","arxiv_id":"2312.03444","date":"2023-12-06","proceeding":null,"authors":["Christian Bayer","Luca Pelizzari","John Schoenmakers"],"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 $L^p-$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.","url_abs":"https://arxiv.org/abs/2312.03444v2","url_pdf":"https://arxiv.org/pdf/2312.03444v2.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"primal-and-dual-optimal-stopping-with","repo_url":"https://github.com/lucapelizzari/optimal_stopping_with_signatures","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null}],"tasks":[],"methods":[{"method_slug":null,"method_name":"American"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}