Abstract
A mathematical model for dynamic portfolio model with uncertainty is discussed. To consider this uncertainty modelling, the randomness and fuzziness are evaluated simultaneously cooperating with both of probabilistic expectation and mean values with λ-weighting functions. By dynamic programming approach, we will derive an optimality equation for the optimal consumption and wealth problem in a fuzzy stochastic process and then an optimal portfolio is given. It is shown that the optimal total expected utility is a solution of the optimality equation under a reasonable assumption.
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