# 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.
Keywords :
Type de document :
Pré-publication, Document de travail
2013
Domaine :

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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
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nonmarkovcontrolFP.pdf
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### Identifiants

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

### Citation

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

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