Computational method of the fuzzy goals at management of a portfolio

In this paper the task of stochastic optimum control of the investor by a portfolio of securities with discrete (with a step in one trade session) time on the given time interval is considered. The final cost of a portfolio is accepted as criterion of a task. The stochastic model of changes of the prices on securities is described by Markovian process with memory; the depth of memory is given. As the control variables of the portfolio the numbers of securities of the different types addressed in the market, included by the investor in the portfolio are considered. The initial amount of the capital is fixed. The management is searched as in a class of program strategies (when the class is set by the functions of time), and in a class synthesis (when the class of possible managements is set by the functions of the current condition of a portfolio and realization of a prices vector). The various forms of commission payments to a stock exchange are considered at operations with securities; the estimations for optimum meanings of criteria in various statements of tasks are established. The methods of the decision of the formulated tasks based on various procedures "fuzziness" of the intermediate purposes are described. The results of calculations for concrete tasks are resulted.