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This paper studies the properties of discrete time stochastic optimal controlproblems associated with portfolio selection. We investigate if optimalcontinuous time strategies can be used effectively for a discrete time marketafter a straightforward discretization. We found that Merton's strategyapproximates the performance of the optimal strategy in a discrete time modelwith the sufficiently small time steps

On asymptotic optimality of Merton's myopic portfolio strategies for discrete time market