By Bruno Bouchard & Nizar Touzi (Cahier de la Chaire n°33)
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-made for the derivation of the dynamic programming equation in the sense of viscosity solutions.
Keywords: Optimal control, Dynamic programming, discontinuous viscosity solutions