Time-average control of martingale problems: the hamilton-jacobi-bellman equation

Abstract

Martingale methods are used to extend the applicability of the Hamilton-Jacobi-Bellman equation to processes given as solutions of a martingale problem. Sufficient conditions are given for both upper and lower bounds on the optimal long-run average cost which are combined to give sufficient conditions under which the HJB equation yields optimality of the cost. Controlled diffusions and controlled queues provide examples of such processes

Keywords:

• Average cost criterion
• martingale problems
• dynamic programming equation
• controlled diffusions
• controlled queues

^*Present address: Department of Mathematics, University of Kentucky, Lexington, KY 40506.

^*Present address: Department of Mathematics, University of Kentucky, Lexington, KY 40506.

Notes

^*Present address: Department of Mathematics, University of Kentucky, Lexington, KY 40506.