{"paper":{"title":"Stochastic Maximum Principle for Mean-field Controls and Non-Zero Sum Mean-field Game Problems for Forward-Backward Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Liangquan Zhang, Ruimin Xu","submitted_at":"2012-07-18T10:17:02Z","abstract_excerpt":"The objective of the present paper is to investigate the solution of fully coupled mean-field forward-backward stochastic differential equations (FBSDEs in short) and to study the stochastic control problems of mean-field type as well as the mean-field stochastic game problems both in which state processes are described as FBSDEs. By combining classical FBSDEs methods introduced by Hu and Peng [Y. Hu, S. Peng, Solution of forward-backward stochastic differential equations, Probab. Theory Relat. Fields 103 (1995)] with specific arguments for fully coupled mean-field FBSDEs, we prove the existen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4326","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"}