| The traditional portfolio theory is founded on a series of strict hypotheses, one of which is the assumption that the investors can change the sort and amount of different securities incorporated in his portfolio freely. However, it's not the case in the reality.The traditional portfolio theory mainly touches on the frictionless market, so in the reality, they don't hold well. Because in fact the transaction cost is not negligible. So the transaction cost should be incorporated in the portfolio model to improve the classical theory.In order to improve the traditional portfolio model's limitations, in this paper, the holding term is evenly divided into many shorter terms, the investors can only trade at the end of each shorter terms, so we can research the optimized investment strategy of the discrete with the help of the classical theory. Besides, in order to satisfy the investors, the model includes the worst-case outcome of the portfolio at the end of the holding term and transaction cost. With that, the investors' objective can be formulated as: U=α U(expected yield ) β U(risk) + (1-α -β )U(the worst-case outcome), So the investors' objective is to obtain the most utility.In the process of finding the answer to the model, Gene Arithmetic is first used to find the optimized answer to each stage, then Nerve Network Arithmetic following to be used to formulate the function between the first parameters and the optimized result, at last, dynamic programming is used to find the most suitable answer to the last end. In order to formulate it explicitly, an example is given in this paper.This paper theoretically formulates a dynamic optimized investment strategy, which incorporates the worst-case outcome and transaction cost. In the process of finding the answer, a lot of difficulties will be encountered. So, this paper gives only the theoretical answer, not but the numeric answer, which is the deficiency of this paper, at the same time, is what I should pursuit in the future. |
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