{"ID":3083711,"CreatedAt":"2026-06-05T06:46:15.197025399Z","UpdatedAt":"2026-06-07T05:49:02.101151534Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2606.06193","arxiv_id":"2606.06193","title":"Peng's Maximum Principle for McKean-Vlasov Stochastic Differential Equations with Common Noise","abstract":"We study a stochastic optimal control problem for McKean-Vlasov stochastic differential equations (SDEs) with common noise, where the dynamics depend on the conditional law of the state. We derive a stochastic maximum principle of Peng type without imposing convexity assumptions on the control domain. In comparison to the standard McKean-Vlasov case, the maximum principle for the common noise case contains a third adjoint state, which is needed to dualize all second-order Lions derivatives in the Taylor expansion of the cost functional. The additional adjoint state is given by a conditional McKean-Vlasov backward SDE. All three adjoint states together allow for a complete linearization of all contributions in the second-order expansion, including interactions between conditionally independent copies of the first variational process. As part of our analysis, we also prove a general well-posedness result for conditional McKean-Vlasov backward SDEs.","short_abstract":"We study a stochastic optimal control problem for McKean-Vlasov stochastic differential equations (SDEs) with common noise, where the dynamics depend on the conditional law of the state. We derive a stochastic maximum principle of Peng type without imposing convexity assumptions on the control domain. In comparison to...","url_abs":"https://arxiv.org/abs/2606.06193","url_pdf":"https://arxiv.org/pdf/2606.06193v1","authors":"[\"Johan Benedikt Spille\",\"Wilhelm Stannat\"]","published":"2026-06-04T14:00:32Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"math.OC\"]","methods":"[]","has_code":false}