A duality approach to problems of combined stopping and deciding under constraints

A problem of combined stopping and deciding under constraints for continuous-time processes on a Brownian filtration is considered. Under certain regularity conditions on the admissible class of stopping times and decision processes it is possible to show that there is no duality gap between the primal constrained optimization problem and the dual problem involving unconstrained minimization and a maximization over Lagrangian multipliers. Copyright Springer-Verlag Berlin Heidelberg 2002