Optimal control of path-dependent McKean-Vlasov SDEs in infinite dimension - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

Optimal control of path-dependent McKean-Vlasov SDEs in infinite dimension

Andrea Cosso
  • Fonction : Auteur
  • PersonId : 1029548
Fausto Gozzi
  • Fonction : Auteur
  • PersonId : 833061
Idris Kharroubi
  • Fonction : Auteur
  • PersonId : 1038223
Mauro Rosestolato
  • Fonction : Auteur
  • PersonId : 1086869

Résumé

We study the optimal control of path-dependent McKean-Vlasov equations valued in Hilbert spaces motivated by non Markovian mean-field models driven by stochastic PDEs. We first establish the well-posedness of the state equation, and then we prove the dynamic programming principle (DPP) in such a general framework. The crucial law invariance property of the value function V is rigorously obtained, which means that V can be viewed as a function on the Wasserstein space of probability measures on the set of continuous functions valued in Hilbert space. We then define a notion of pathwise measure derivative, which extends the Wasserstein derivative due to Lions [41], and prove a related functional Itô formula in the spirit of Dupire [24] and Wu and Zhang [51]. The Master Bellman equation is derived from the DPP by means of a suitable notion of viscosity solution. We provide different formulations and simplifications of such a Bellman equation notably in the special case when there is no dependence on the law of the control.
Fichier principal
Vignette du fichier
CGKPR-5Dic21.pdf (732.56 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03088371 , version 1 (26-12-2020)
hal-03088371 , version 2 (06-12-2022)

Identifiants

Citer

Andrea Cosso, Fausto Gozzi, Idris Kharroubi, Huyên Pham, Mauro Rosestolato. Optimal control of path-dependent McKean-Vlasov SDEs in infinite dimension. 2020. ⟨hal-03088371v2⟩
125 Consultations
173 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More