Classes of preferences of portfolio investors for multi-period case and their asymptotic properties

Methods for the definition of preferences of portfolio investors for the multi-period investment horizon are considered and the dependence of investor behavior on the horizon length is studied. It is assumed that the capitalization share of each portfolio security doesn't vary in time. Hence, portfolio restructuring on each step of the investment process is necessary to allocate the whole portfolio value between the component securities in a proportion chosen by the investor. It is supposed that the restructuring transaction costs are equal to zero. In portfolio theory, different approaches are used. In this paper, three of them are considered. The first involves the definition of the effective portfolio set, the second involves the concept of indifference curves and the third involves drawdown criteria.