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BSDE formulation of combined regular and singular stochastic control problems

Bouchard, Bruno; Cheridito, Patrick; Hu, Ying (2018), BSDE formulation of combined regular and singular stochastic control problems. https://basepub.dauphine.fr/handle/123456789/17925

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Type
Document de travail / Working paper
Date
2018
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Pages
11
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Author(s)
Bouchard, Bruno
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Cheridito, Patrick
Department of Mathematics [ETH Zurich] [D-MATH]
Hu, Ying
Institut de Recherche Mathématique de Rennes [IRMAR]
Abstract (EN)
In this paper we study a class of combined regular and singular stochastic control problems that can be expressed as constrained BSDEs. In the Markovian case, this reduces to a characterization through a PDE with gradient constraint. But the BSDE formulation makes it possible to move beyond Markovian models and consider path-dependent problems. We also provide an approximation of the original control problem with standard BSDEs that yield a characterization of approximately optimal values and controls.
Subjects / Keywords
minimal supersolution; singular stochastic control; constraint backward stochastic differential equation