Optimal control of the portfolio

Consideration was given to the optimal control of the bilinear system descr ibing the investments in securities of two kinds. The exchange paradox caus ed by an unsuccessful choice of the optimality criterion in the form of mea n 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 o f securities on the basis of the confidence method and sampling of the prob abilistic measure was proposed. Its efficiency as compared with the risk an d logarithmic strategies was estimated by way of a model example.