Before revision: The paper studies the properties of discrete time stochastic optimal control problems associated with the portfolio selectionproblem and related continuous time portfolio selection problems. We found that Merton's strategy that is optimal for continuous time model can be used effectively for the discrete market model that has sufficiently small time steps and approximate the continuous time model.
After revision: The paper studies the properties of discrete time stochastic optimal control problems associated with portfolio selection. We investigate if optimal continuous time strategies can be used effectively for the discrete market model that has sufficiently small time steps and approximate the continuous time model.