On the Construction of Positional Control in a Multistep Portfolio Optimization Problem with Probabilistic Criterion

We consider a multistep portfolio optimization problem. At every time step, capital can be invested either in a risk-free asset with fixed income or in a risky asset with a random return with a finite density. The optimality criterion is the probability of reaching or exceeding the investor’s capital at the terminal time moment at a certain predetermined level. Based on the use of piecewise constant control, we propose a positional control that surpasses previously known universal controls, which are used in portfolio optimization problems, in terms of the value of the probabilistic criterion on a wide set of examples.