A Novel Approach to Peng's Maximum Principle for McKean-Vlasov Stochastic Differential Equations
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918334520360960 |
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| author | Spille, Johan Benedikt Stannat, Wilhelm |
| author_facet | Spille, Johan Benedikt Stannat, Wilhelm |
| contents | We present a novel approach to the proof of Peng's maximum principle for McKean-Vlasov stochastic differential equations (SDE). The main step is the introduction of a third adjoint equation, a conditional McKean-Vlasov backward SDE, to accommodate the dualization of quadratic terms containing two independent copies of the first-order variational process. This is an intrinsic extension of the maximum principle from Peng for standard SDE and gives a conceptually consistent proof. Our approach will be useful in further extensions to the common noise setting and the infinite dimensional setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12006 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Novel Approach to Peng's Maximum Principle for McKean-Vlasov Stochastic Differential Equations Spille, Johan Benedikt Stannat, Wilhelm Probability Optimization and Control 93E20, 49K45, 49N80 (Primary) 60H30, 60H10, 49N15 (Secondary) We present a novel approach to the proof of Peng's maximum principle for McKean-Vlasov stochastic differential equations (SDE). The main step is the introduction of a third adjoint equation, a conditional McKean-Vlasov backward SDE, to accommodate the dualization of quadratic terms containing two independent copies of the first-order variational process. This is an intrinsic extension of the maximum principle from Peng for standard SDE and gives a conceptually consistent proof. Our approach will be useful in further extensions to the common noise setting and the infinite dimensional setting. |
| title | A Novel Approach to Peng's Maximum Principle for McKean-Vlasov Stochastic Differential Equations |
| topic | Probability Optimization and Control 93E20, 49K45, 49N80 (Primary) 60H30, 60H10, 49N15 (Secondary) |
| url | https://arxiv.org/abs/2602.12006 |