Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) for Solving Nonlinear Option Pricing models

Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) for Solving Nonlinear Option Pricing models | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) for Solving Nonlinear Option Pricing models Qinjiao Gao, Zuowei Wang, Ran Zhang, Dongjiang Wang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6342158/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 9 You are reading this latest preprint version Abstract In this paper, we propose the Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) to address challenges in solving nonlinear option pricing PDE models, where solutions often exhibit significant curvature or shock waves over time. The AM-PIRN architecture is designed to concurrently minimize PDE residuals and achieve high-fidelity option price approximations by dynamically redistributing training points based on evolving PDE residuals, while maintaining a fixed total number of points. To enhance stability and training efficiency, we integrate a ResNet backbone, replacing conventional fully connected neural networks used in Physics-Informed Neural Networks (PINNs). Numerical experiments across nonlinear option pricing models demonstrate that AM-PIRN outperforms PINN, RAM-PINN, and WAM-PINN in both resolving PDE constraints and accurately estimating option prices. The method’s advantages are particularly pronounced in complex or multi-dimensional models, where its adaptive sampling and robust architecture effectively mitigate challenges posed by sharp gradients and high nonlinearity. AMS Subject Classifications: 41A05, 65M50, 91G20, 68T07. ResNet Option pricing model Adaptive sampling Physics-informed neural networks (PINNs) Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Revision requested 10 Nov, 2025 Reviews received at journal 10 Nov, 2025 Reviews received at journal 03 Nov, 2025 Reviewers agreed at journal 09 Aug, 2025 Reviewers agreed at journal 07 Aug, 2025 Reviewers invited by journal 14 May, 2025 Editor assigned by journal 02 Apr, 2025 Submission checks completed at journal 02 Apr, 2025 First submitted to journal 31 Mar, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6342158","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":456936580,"identity":"4d5e4f41-584b-4b11-904f-fcba62b391c1","order_by":0,"name":"Qinjiao Gao","email":"","orcid":"","institution":"Zhejiang Gongshang University","correspondingAuthor":false,"prefix":"","firstName":"Qinjiao","middleName":"","lastName":"Gao","suffix":""},{"id":456936585,"identity":"009c7495-2d7c-4869-bfe2-546c82c92305","order_by":1,"name":"Zuowei Wang","email":"","orcid":"","institution":"Zhejiang Gongshang University","correspondingAuthor":false,"prefix":"","firstName":"Zuowei","middleName":"","lastName":"Wang","suffix":""},{"id":456936587,"identity":"378f7f06-0b33-4397-b1ab-a850559f7ca2","order_by":2,"name":"Ran Zhang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABI0lEQVRIie3RMUvEMBTA8RcK7VL3V07pV4gcXIVT+lUSMnRpVRCkg0NBuNX14PwQgULhtgOht7R7D0FOBBeXDiKdxEQUHFq90SH/KaH5kUcKYDL9x/B74WQA7ByAAtmqrbUDcVeKUE0suiNBBvr838RfXD8/vsKDH3gvvN1SCAMUarJ0yjOnXvURclsG4324OFwukhzVYHw5F+qaKuKZe8r6iIVsMkJgRN4nUhNGm7MSyeyOZ+jSPmJj9KZJKDd13ikS0kY4HXkfJi7GE68FxmWzV+hbiGyEDSQbJojx5QgoE7JKiiNGkcvqSU1bRuOZG/cSfx4VXpeyE7mu802XHod0LUjbXk0Pbpyql3w+wY8Bvn6Tfip76LyKdL98NJlMJhN8AIjLWpeFg+kUAAAAAElFTkSuQmCC","orcid":"","institution":"Shanghai University of Finance and Economics","correspondingAuthor":true,"prefix":"","firstName":"Ran","middleName":"","lastName":"Zhang","suffix":""},{"id":456936588,"identity":"d04342bc-3df7-462d-a9af-ff19a6a5838d","order_by":3,"name":"Dongjiang Wang","email":"","orcid":"","institution":"Zhejiang Gongshang University","correspondingAuthor":false,"prefix":"","firstName":"Dongjiang","middleName":"","lastName":"Wang","suffix":""}],"badges":[],"createdAt":"2025-03-31 06:39:35","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6342158/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6342158/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":82976892,"identity":"0d2ce3e6-11c8-48d8-a4ad-cdf7ff675ded","added_by":"auto","created_at":"2025-05-18 08:52:29","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2130715,"visible":true,"origin":"","legend":"","description":"","filename":"AMPIRN.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6342158/v1_covered_22ec7f6d-60ea-48d9-8189-020856b1ad5d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) for Solving Nonlinear Option Pricing models","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":false,"email":"[email protected]","identity":"optimization-and-engineering","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"11081","submissionUrl":"https://submission.nature.com/new-submission/11081/3","title":"Optimization and Engineering","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"ResNet, Option pricing model, Adaptive sampling, Physics-informed neural networks (PINNs)","lastPublishedDoi":"10.21203/rs.3.rs-6342158/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6342158/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn this paper, we propose the Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) to address challenges in solving nonlinear option pricing PDE models, where solutions often exhibit significant curvature or shock waves over time. 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