On asymptotic optimality of Merton's myopic portfolio strategies for   discrete time market
  This 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 a discrete time market after a straightforward discretization. We found that Merton's strategy approximates the performance of the optimal strategy in a discrete time model with the sufficiently small time steps 
Alexandra Rodkina and Nikolai Dokuchaev
q-fin.PM math.OC