Entropy-Regularized Entropic Recursive Utility in Complete Black-Scholes Markets

Entropy-Regularized Entropic Recursive Utility in Complete Black-Scholes Markets | 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 Entropy-Regularized Entropic Recursive Utility in Complete Black-Scholes Markets WonChan Cho This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8760642/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper studies continuous-time consumption-investment decisions in a complete multi-asset Black-Scholes market under \emph{entropic recursive utility} represented by a quadratic BSDE. To incorporate robustness and exploration in the control layer, portfolio choice is formulated as an \emph{entropy-regularized relaxed control} relative to a Gaussian reference prior. By applying the Donsker-Varadhan variational formula, the resulting dynamic programming equation admits a \emph{soft Hamiltonian} of log-sum-exp type, and the optimal relaxed portfolio is characterized by an explicit \emph{Gibbs tilt} of the prior. Under log utility, we derive a closed-form Markovian ansatz for the value function and reduce the associated soft HJB equation to a system of scalar ODEs. We then provide a verification theorem under explicit well-posedness and admissibility conditions tailored to quadratic BSDE preferences, including BMO-martingale requirements for the candidate martingale integrand. Finally, we outline and numerically validate an extension to Epstein-Zin recursive preferences via a Deep BSDE solver that preserves the entropy-regularized structure beyond the log closed-form benchmark, together with stability diagnostics and risk-return sensitivity modes. Financial Mathematics Entropic recursive utility quadratic BSDE entropy-regularized control soft HJB Donsker-Varadhan relaxed portfolio choice Epstein-Zin Deep BSDE Full Text Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted 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-8760642","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":584027654,"identity":"df37967c-19a5-44dd-8946-4cd86fd5e1b8","order_by":0,"name":"WonChan Cho","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAx0lEQVRIiWNgGAWjYDACCeYGhgQDG2Z+BjZmEJ+xgbAWoJoPBWnskg2kaGGc8eEwv8EBYrXwz25se8xjwCxtfP5YsjEPg43shgOELLlzsN2Yx4DN2OxG2uFkHoY0Y4JaDCQS26R5DHiSzW6wNx/mYTicSKwWifrN/cdBWv4Tp0VyhoEBswED2GEHCGuRuJHYJvHBIIFZ4kZasuEcg2TjmYS08M9IPiaR8Oc/M3//MWOJNxV2sn2EtKC7kzTlo2AUjIJRMApwAAAnvD/MYPUFYQAAAABJRU5ErkJggg==","orcid":"","institution":"Sungkyunkwan University, Department of Mathematics","correspondingAuthor":true,"prefix":"","firstName":"WonChan","middleName":"","lastName":"Cho","suffix":""}],"badges":[],"createdAt":"2026-02-02 05:11:41","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8760642/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8760642/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":101753905,"identity":"d82bc0ed-3da1-4117-b15a-6a66706d4334","added_by":"auto","created_at":"2026-02-03 10:41:09","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1075189,"visible":true,"origin":"","legend":"","description":"","filename":"EntropyRegularizedEntropicRecursiveUtilityinCompleteBlackScholesMarkets.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8760642/v1_covered_b74f12a5-65df-4139-b094-23fac3640ac3.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eEntropy-Regularized Entropic Recursive Utility in Complete Black-Scholes Markets\u003c/p\u003e","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Entropic recursive utility, quadratic BSDE, entropy-regularized control, soft HJB, Donsker-Varadhan, relaxed portfolio choice, Epstein-Zin, Deep BSDE","lastPublishedDoi":"10.21203/rs.3.rs-8760642/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8760642/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper studies continuous-time consumption-investment decisions in a complete multi-asset Black-Scholes market under \\emph{entropic recursive utility} represented by a quadratic BSDE. 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