PARAMETRIC CONTINUITY IN DYNAMIC-PROGRAMMING PROBLEMS

We examine conditions under which the solutions to parametric families of dynamic programming problems are continuous in the parameters. Our main results are that parametric continuity obtains whenever either (a) the family of dynamic programming problems satisfies strong (joint-) continuity properties in the parameter and state or (b) if it satisfies weaker (separate-) continuity requirements, provided these are supplemented by either stronger assumptions on the transition probabilities or by monotonicity restrictions such as are common in economic modelling. The usefulness of our results is illustrated by applying them to some commonly used dynamic economic models.