On nontraditional problems of portfolio management

Some applications of portfolio investment theory, which goes back to papers by H. Markowitz and J. Tobin, are considered. First, problems of the dynamic control of an investment portfolio are considered in the case when the behavior of the average characteristics of returns on assets is described not by stochastic differential equations but by deterministic differential inclusions. Such a description of the uncertainty allows one to apply methods of the theory of guaranteed control and the theory of positional differential games. Second, it is shown how the theory developed initially for portfolios of of risk financial instruments (shares) can be used, after an appropriate modification, for studying objects of different nature as well. In particular, problems of constructing an effective project portfolio and effective portfolios of contractors and clients of a firm are considered.