A randomisation method for mean-field control problems with common noise
Résumé
We study mean-field control (MFC) problems with common noise using the control randomisation framework, where we substitute the control process with an independent Poisson point process, controlling its intensity instead. To address the challenges posed by the mean-field interactions in this randomisation approach, we reformulate the admissible control as L 0 -valued processes adapted only to the common noise. We then construct the randomised control problem from this reformulated control process, and show its equivalence to the original MFC problem. Thanks to this equivalence, we can represent the value function as the minimal solution to a backward stochastic differential equation (BSDE) with constrained jumps. Finally, using this probabilistic representation, we derive a randomised dynamic programming principle (DPP) for the value function, expressed as a supremum over equivalent probability measures.
Mots clés
Mean-field control with common noise
control randomisation
decomposition of processes
randomised dynamic programming principle
backward stochastic differential equations
MSC Classification: 60H30 60K35 60K37 93E20 Mean-field control with common noise control randomisation decomposition of processes randomised dynamic programming principle backward stochastic differential equations
MSC Classification: 60H30
60K35
60K37
93E20 Mean-field control with common noise
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