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 natural discretization, the Merton's strategy approximates the performance of the optimal strategy in  discrete time model .
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
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the portfolio selectionproblem and related continuous time portfolio selection problems. We found that Merton's strategy that is optimal for continuous time model
portfolio selection. We investigate if optimal continuous time strategies
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the discrete market model that has sufficiently small time steps and approximate the continuous time model. After natural discretization, the
a discrete time market after a straightforward discretization. We found that
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with the sufficiently small time steps