Before revision:  We thus close a duality gap encountered by Vellekoop and Davis in an infinite horizon version of this problem . Nearly all the classical tenets of duality theory are found to hold, with the notable exception that the marginal utility of initial wealth at zero is finite.
After revision:  We thus close a duality gap encountered by Vellekoop and Davis in an infinite horizon version of this problem in a Black-Scholes market. Many of the classical tenets of duality theory are found to hold, with the notable exception that the marginal utility of initial wealth at zero is finite.