Optimal Control of the Portfolio

Consideration was given to the optimal control of the bilinear system describing the investments in securities of two kinds. The exchange paradox caused by an unsuccessful choice of the optimality criterion in the form of mean income was discussed. One way around this problem is to use the value of the capital guaranteed with a given probability as the optimality criterion. To handle the arising problem, a new strategy of building the portfolio of securities on the basis of the confidence method and sampling of the probabilistic measure was proposed. Its efficiency as compared with the risk and logarithmic strategies was estimated by way of a model example.