Optimal Control of the Investment Portfolio with Respect to the Quantile Criterion

A two-step problem is considered for the optimal portfolio investment management (control) involving two kinds of securities with respect to the quantile criterion under the assumption of the uniform distribution of the return. The problem with the quantile criterion reduces to optimization of a probability functional, and for the analytical synthesis of an optimal strategy, use is made of a method of dynamic programming. The effectiveness of the suggested strategy in comparison with other known strategies of portfolio control is illustrated by an example.