{"paper":{"title":"Dynamic Programming for General Linear Quadratic Optimal Stochastic Control with Random Coefficients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Shanjian Tang","submitted_at":"2014-07-18T15:16:51Z","abstract_excerpt":"We are concerned with the linear-quadratic optimal stochastic control problem with random coefficients. Under suitable conditions, we prove that the value field $V(t,x,\\omega), (t,x,\\omega)\\in [0,T]\\times R^n\\times \\Omega$, is quadratic in $x$, and has the following form: $V(t,x)=\\langle K_tx, x\\rangle$ where $K$ is an essentially bounded nonnegative symmetric matrix-valued adapted processes. Using the dynamic programming principle (DPP), we prove that $K$ is a continuous semi-martingale of the form $$K_t=K_0+\\int_0^t \\, dk_s+\\sum_{i=1}^d\\int_0^tL_s^i\\, dW_s^i, \\quad t\\in [0,T]$$ with $k$ bein"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5031","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}