Convexity in stochastic control (Q5943514)

This article surveys the convex analytic formulations of control problems for controlled stochastic differential equations. The author recasts the dynamic control problem as a static optimization problem on an appropriately defined convex set of measures. Applying the convex analytic approach, he presents the following results: (1) the existence theory of optimal control, via suitable characterization of extremal measures; (2) the value function of dynamic programming can be recovered as the maximal subsolution of dynamic programming inequalities, via dualization: (3) these arguments yield new results in some nonclassical problems.