BSDE formulation of combined regular and singular stochastic control problems

Bruno Bouchard (1) , Patrick Cheridito (2) , Ying Hu (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 D-MATH - Department of Mathematics [ETH Zurich]
3 IRMAR - Institut de Recherche Mathématique de Rennes

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.

Mots clés: singular stochastic control; constraint backward stochastic differential equation; minimal supersolution

Domaines: Optimisation et contrôle [math.OC]

Bruno Bouchard, Patrick Cheridito, Ying Hu. BSDE formulation of combined regular and singular stochastic control problems. 2018. ⟨hal-01679138⟩