{"paper":{"title":"Indefinite Stochastic LQ Optimal Control for Jump-Diffusion Systems with Random Coefficients","license":"http://creativecommons.org/licenses/by/4.0/","headline":"Under a uniform convexity condition, indefinite stochastic LQ optimal controls exist for jump-diffusion systems with random coefficients and admit closed-loop feedback representations.","cross_cats":[],"primary_cat":"math.OC","authors_text":"Qingxin Meng, Xinyu Ma","submitted_at":"2026-05-12T21:41:32Z","abstract_excerpt":"This paper studies indefinite stochastic linear-quadratic (LQ) optimal control for jump-diffusion systems with random coefficients. We construct an algebraic inverse flow from the zero-control base system, extract the semimartingale kernel of the value function, and prove that it satisfies a generalized stochastic Riccati equation with jumps (SREJ). Under a uniform convexity condition, we establish the existence and uniqueness of open-loop optimal controls for any initial pair and show that the associated matrix $\\mathscr{N}(t)$ is uniformly positive definite, yielding an exact closed-loop fee"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"Under a uniform convexity condition, we establish the existence and uniqueness of open-loop optimal controls for any initial pair and show that the associated matrix N(t) is uniformly positive definite, yielding an exact closed-loop feedback representation of the optimal control via the SREJ.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The uniform convexity condition must hold globally so that the matrix N(t) remains uniformly positive definite; if it fails for some paths, the existence and closed-loop representation may not hold.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"The paper proves existence and uniqueness of optimal controls for indefinite LQ problems in jump-diffusion systems with random coefficients by constructing a generalized stochastic Riccati equation with jumps from an algebraic inverse flow, under uniform convexity.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"Under a uniform convexity condition, indefinite stochastic LQ optimal controls exist for jump-diffusion systems with random coefficients and admit closed-loop feedback representations.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"d4f9af241e4d035285d1774be476c88e3ffead1fa3dd6a7637ee40092d7015a7"},"source":{"id":"2605.12775","kind":"arxiv","version":1},"verdict":{"id":"52b46485-d882-40eb-afa5-e0f67d12feb2","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T20:01:07.220149Z","strongest_claim":"Under a uniform convexity condition, we establish the existence and uniqueness of open-loop optimal controls for any initial pair and show that the associated matrix N(t) is uniformly positive definite, yielding an exact closed-loop feedback representation of the optimal control via the SREJ.","one_line_summary":"The paper proves existence and uniqueness of optimal controls for indefinite LQ problems in jump-diffusion systems with random coefficients by constructing a generalized stochastic Riccati equation with jumps from an algebraic inverse flow, under uniform convexity.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The uniform convexity condition must hold globally so that the matrix N(t) remains uniformly positive definite; if it fails for some paths, the existence and closed-loop representation may not hold.","pith_extraction_headline":"Under a uniform convexity condition, indefinite stochastic LQ optimal controls exist for jump-diffusion systems with random coefficients and admit closed-loop feedback representations."},"references":{"count":45,"sample":[{"doi":"10.1007/978-0-8176-4757-5","year":2008,"title":"Basar, T. and Bernhard, P. (2008). H-infinity Optimal Control and Related Minimax Design Problems: A Dynamic Game Approach. Springer Science & Business Media. https://doi.org/10.1007/978-0-8176-4757-5","work_id":"bcc8dfea-589f-4db3-93d2-34d55b095f60","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1137/0314028","year":1976,"title":"Bismut, J. M. (1976). Linear quadratic optimal stochastic control with random coefficients. SIAM J. Control Optim., 14:419--444. https://doi.org/10.1137/0314028","work_id":"9eccfd48-3d64-480b-9c29-aa6990e472c7","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1137/0318038","year":1980,"title":"Boel, R. and Kohlmann, M. (1980). Semi-martingale models of stochastic optimal control, with applications to double martingales. SIAM J. Control Optim., 18:511--533. https://doi.org/10.1137/0318038","work_id":"0cb99692-fac0-4abd-8e66-228079164f69","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1137/s0363012996310478","year":1998,"title":"Chen, S., Li, X. and Zhou, X. Y. (1998). Stochastic linear quadratic regulators with indefinite control weight costs. SIAM J. Control Optim., 36:1685--1702. https://doi.org/10.1137/S0363012996310478","work_id":"f4a8b4a1-2b4b-4f97-853d-a5ce828a877f","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1137/140956051","year":2015,"title":"Du, K. (2015). Solvability conditions for indefinite linear quadratic optimal stochastic control problems and associated stochastic Riccati equations. SIAM J. Control Optim., 53:3673--3689. https://do","work_id":"e1896965-bfdb-4a78-ab66-10506bf78451","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":45,"snapshot_sha256":"8a374eee912bdf945aa085cd4611e4d5cd85b9b4e84ed9662611c2f99e499bab","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"fda20e6dad1efaadbafa1a01cfb3d24b91a85bc9a814948c9cf47863d8a2d380"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}