Differentiability of the value function in continuous-time economic models

In this paper we provide some sufficient conditions for the differentiability of the value function in a class of infinite-horizon continuous-time models of convex optimization arising in economics. We dispense with the assumption of interior optimal paths. This assumption is quite unnatural in constrained optimization, and is usually hard to check in applications. The differentiability of the value function is used to prove Bellman’s equation as well as the existence and continuity of the optimal feedback policy. We also establish the uniqueness of the vector of dual variables. These results become useful for the characterization and computation of optimal solutions.This paper was written while Manuel Santos was visiting Universidad Carlos III de Madrid. We acknowledge financial support from projects SEJ2005- 05831, ECO2008-04073 and ECO2008-02358 of the Spanish Ministry of Science and Innovation, and a Cátedra de Excelencia of Banco Santander.Publicad