Stochastic optimality in the portfolio tracking problem involving investor’s temporal preferences

We consider an optimal portfolio selection problem to track a riskless reference portfolio. Portfolio management strategies are compared taking into account the investor’s temporal preferences. We investigate stochastic optimality of the strategy that minimizes the expected long‐run cost, deriving an asymptotical upper (almost sure) estimate for the difference between the values of the objective functional corresponding to the optimal strategy and for any admissible control.