Dual and backward SDE representation for optimal control of non-Markovian SDEs

Abstract : We study optimal stochastic control problem for non-Markovian stochastic differential equations (SDEs) where the drift, diffusion coefficients, and gain functionals are path-dependent, and importantly we do not make any ellipticity assumption on the SDE. We develop a controls randomization approach, and prove that the value function can be reformulated under a family of dominated measures on an enlarged filtered probability space. This value function is then characterized by a backward SDE with nonpositive jumps under a single probability measure, which can be viewed as a path-dependent version of the Hamilton-Jacobi-Bellman equation, and an extension to $G$ expectation.
Type de document :
Pré-publication, Document de travail
2013
Liste complète des métadonnées


https://hal.archives-ouvertes.fr/hal-00876957
Contributeur : Huyen Pham <>
Soumis le : vendredi 25 octobre 2013 - 14:49:42
Dernière modification le : lundi 29 mai 2017 - 14:21:56
Document(s) archivé(s) le : lundi 27 janvier 2014 - 13:11:12

Fichiers

nonmarkovcontrolFP.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

  • HAL Id : hal-00876957, version 1
  • ARXIV : 1310.6943

Collections

INSMI | UPMC | PMA | USPC

Citation

Marco Fuhrman, Huyen Pham. Dual and backward SDE representation for optimal control of non-Markovian SDEs. 2013. <hal-00876957>

Partager

Métriques

Consultations de
la notice

535

Téléchargements du document

312