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Daily Overview |
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Sto1: Stochastic analysis and differential equations Location: L602 Session Chair: Alexandra Blessing | |
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Peng's Maximum Principle for McKean-Vlasov Stochastic Differential Equations with Common Noise TU Berlin, Germany 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 introduced in [1], which is needed to dualize all second-order Lions derivatives in the Taylor expansion of the cost functional. This 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. As part of our analysis, we also prove a general well-posedness result for conditional McKean-Vlasov backward SDEs. The talk is based on joint work with J. Spille (TU Berlin). [1] J. Spille, W. Stannat: A Novel Approach to Peng's Maximum Principle for McKean-Vlasov Stochastic Differential Equations, arXiv:2602.12006 [2] J. Spille, W. Stannat: Peng's Maximum Principle for McKean-Vlasov Stochastic Differential Equations with Common Noise, arXiv:2606.06193 | |
