Monotocity and bounds for convex stochastic control models

The authors consider a general convex stochastic control model. Their main interest concerns monotonicity results and bounds for the value functions and for optimal policies. In particular, the authors show how the value functions depend on the transition kernels and they present conditions for a lower bound of an optimal policy. The present approach is based on convex stochastic orderings of probability measures. The authors derive several interesting sufficient conditions of these ordering concepts, where they make also use of the Blackwell ordering. The structural results are illustrated by partially observed control models and Bayesian information models.