{"paper":{"title":"Extended MF-FBSDEs with nonlinear domination-monotonicity conditions and stochastic optimal controls of Linear System with quadruple controls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"Nonlinear adjoint functions extend domination-monotonicity conditions to guarantee well-posedness of extended mean-field FBSDEs and deliver explicit optimal controls for linear systems with quadruple inputs.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Hao Wu","submitted_at":"2026-05-10T06:57:51Z","abstract_excerpt":"This paper extends the domination-monotonicity conditions, which guarantee the well-posedness of extended mean-filed forward-backward stochastic differential equations (extended MF-FBSDEs), from the previously studied linear framework to a nonlinear setting by incorporating nonlinear adjoint functions. Utilizing this generalized well-posedness result for extended MF-FBSDEs in conjunction with other refined analytical techniques, we address two classes of stochastic quadruple optimal controlled problems: a linear-convex problem and a linear-quadratic problem with input constraints that are perm"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Utilizing this generalized well-posedness result for extended MF-FBSDEs in conjunction with other refined analytical techniques, we address two classes of stochastic quadruple optimal controlled problems: a linear-convex problem and a linear-quadratic problem with input constraints that are permitted to be time-dependent and random. For each problem, we establish the existence and uniqueness of optimal controls and derive their explicit closed-form representations.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The nonlinear domination-monotonicity conditions, defined via nonlinear adjoint functions, are sufficient to guarantee well-posedness of the extended MF-FBSDEs.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Extends domination-monotonicity conditions to nonlinear extended MF-FBSDEs and derives closed-form optimal controls for linear-convex and linear-quadratic stochastic control problems with time-dependent random input constraints.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Nonlinear adjoint functions extend domination-monotonicity conditions to guarantee well-posedness of extended mean-field FBSDEs and deliver explicit optimal controls for linear systems with quadruple inputs.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"6b27126b4f4b987abcfda3bfc82382a4848cee3901989ef9750142ccdb51224a"},"source":{"id":"2605.09374","kind":"arxiv","version":2},"verdict":{"id":"8cf08fd7-7337-414d-ad35-755af6c3da00","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-12T04:39:27.170339Z","strongest_claim":"Utilizing this generalized well-posedness result for extended MF-FBSDEs in conjunction with other refined analytical techniques, we address two classes of stochastic quadruple optimal controlled problems: a linear-convex problem and a linear-quadratic problem with input constraints that are permitted to be time-dependent and random. For each problem, we establish the existence and uniqueness of optimal controls and derive their explicit closed-form representations.","one_line_summary":"Extends domination-monotonicity conditions to nonlinear extended MF-FBSDEs and derives closed-form optimal controls for linear-convex and linear-quadratic stochastic control problems with time-dependent random input constraints.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The nonlinear domination-monotonicity conditions, defined via nonlinear adjoint functions, are sufficient to guarantee well-posedness of the extended MF-FBSDEs.","pith_extraction_headline":"Nonlinear adjoint functions extend domination-monotonicity conditions to guarantee well-posedness of extended mean-field FBSDEs and deliver explicit optimal controls for linear systems with quadruple inputs."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.09374/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T07:42:01.505995Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"ai_meta_artifact","ran_at":"2026-05-19T19:36:35.989000Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_title_agreement","ran_at":"2026-05-19T13:01:18.425937Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T10:19:36.145504Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"e5f1539213be55049f8eaeea874f14478eea9c03ddf4b455fbbbd88e3564a4bc"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}