Weak Dynamic Programming Principle for Viscosity Solutions

Bruno Bouchard (1, 2) , Nizar Touzi (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 CREST - Centre de Recherche en Économie et Statistique
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique

We prove a weak version of the dynamic programming principle for standard stochastic control problems and mixed control-stopping problems, which avoids the technical difficulties related to the measurable selection argument. In the Markov case, our result is tailor-maid for the derivation of the dynamic programming equation in the sense of viscosity solutions.

Mots clés: Optimal control; Dynamic programming; Discontinuous viscosity solutions

Domaines: Probabilités [math.PR]

Bruno Bouchard, Nizar Touzi. Weak Dynamic Programming Principle for Viscosity Solutions. SIAM Journal on Control and Optimization, 2011, 49 (3), pp.948-962. ⟨hal-00367355v4⟩