  This paper is devoted to the analysis of a finite horizon discrete-time
stochastic optimal control problem, in presence of constraints. We study the
regularity of the value function which comes from the dynamic programming
algorithm. We derive accurate estimates of the Lipschitz constant of the value
function, by means of a regularity result of the multifunction that defines the
admissible control set. In the last section we discuss an application to an
optimal asset-allocation problem.
