{"ID":23475052,"CreatedAt":"2026-09-18T01:09:05.407443952Z","UpdatedAt":"2026-09-20T18:11:56.143995915Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2609.19779","arxiv_id":"2609.19779","title":"Extended MF-AFBSDDEswCN and stochastic optimal controls of linear system","abstract":"The research studies the extended mean-field anticipated forward-backward stochastic delayed differential equations with common noise (extended MF-AFBSDDEswCN) by expanding the domination-monotonicity conditions. We generalize the conditions from a linear setting to a nonlinear one by including nonlinear adjoint functions which are key to guaranteeing the well-posedness of extended MF-AFBSDDEswCN. Utilizing this broader well-posedness framework for extended MF-AFBSDDEswCN, combined with other refined analytical tools, we examine two classes of stochastic optimal control problems. These include a linear-convex problem and a linear-quadratic problem with input constraints that can be both time-dependent and random. Moreover, the control elements regarding the initial values are path-dependent, which will cause some essential difficulties. For each problem, we establish the existence and uniqueness of optimal controls and provide their explicit, closed-form representations.","short_abstract":"The research studies the extended mean-field anticipated forward-backward stochastic delayed differential equations with common noise (extended MF-AFBSDDEswCN) by expanding the domination-monotonicity conditions. We generalize the conditions from a linear setting to a nonlinear one by including nonlinear adjoint functi...","url_abs":"https://arxiv.org/abs/2609.19779","url_pdf":"https://arxiv.org/pdf/2609.19779v1","authors":"[\"Hao Wu\"]","published":"2026-09-17T06:46:10Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}