Optimal Control versus Stochastic Target problems: An Equivalence Result

Bruno Bouchard (1, 2) , Minh Ngoc Dang (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CREST - Centre de Recherche en Économie et Statistique

Within a general abstract framework, we show that any optimal control problem in standard form can be translated into a stochastic target problem as defined in Soner and Touzi (2002), whenever the underlying filtered probability space admits a suitable martingale representation property. This provides a unified way of treating these two classes of stochastic control problems. As an illustration, we show, within a jump diffusion framework, how the Hamilton-Jacobi-Bellman equations associated to an optimal control problem in standard form can be easily retrieved from the partial differential equations associated to its stochastic target counterpart.

Mots clés: Stochastic target; Stochastic control; Viscosity solutions.; Viscosity solutions

Domaines: Probabilités [math.PR]

Bruno Bouchard, Minh Ngoc Dang. Optimal Control versus Stochastic Target problems: An Equivalence Result. Systems and Control Letters, 2012, 61 (2), pp.343-346. ⟨10.1016/j.sysconle.2011.11.010⟩. ⟨hal-00556509⟩