A randomisation method for mean-field control problems with common noise - Archive ouverte HAL
Pré-Publication, Document De Travail (Preprint/Prepublication) Année : 2024

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.
Fichier principal
Vignette du fichier
randomisation_method_mfc.pdf (568.42 Ko) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04855029 , version 1 (30-12-2024)

Licence

Domaine public

Identifiants

Citer

Robert Denkert, Idris Kharroubi, Huyên Pham. A randomisation method for mean-field control problems with common noise. 2024. ⟨hal-04855029⟩
0 Consultations
0 Téléchargements

Altmetric

Partager

More