Maximizing the time until a controlled random walk in the quadrant hits the boundary

At every moment the control acts on only one of the two coordinates of the random walk with a fixed impact. A strategy, optimal for a whole family of criteria (mean hitting time, probability of never hitting, and so on) has been found. Solving the Bellman equation has been avoided owing to favorable properties of the model: symmetry, monotonicity, decomposability. The model has arisen while studying economic problems.