Stochastic optimal policies when the discount rate vanishes

Dutta [1991. What do discounted optima converge to? A theory of discount rate asymptotics in economic models. Journal of Economic Theory 55, 64-94] showed that long-run optimality of the limit of discounted optima when the discount rate vanishes is implied by a certain bound on the value function of the optimal program. We introduce a new method to verify this bound using coupling techniques.