Condition of degeneration of optimal instant in the problem of optimal stopping for a new functional on symmetric random walking and its maximum / *A. L. Vorob'ev.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 4. P. 3-13
[Moscow Univ. Math. Bulletin. Vol. 72, N 2, 2017. P. 149-159].

New classes of functionals are proposed for an optimal stopping problem for a functional of a symmetric random walk and its maximum. For one class the optimal moment in a finite time interval is the beginning of this interval and for another one this is its end. These classes generalize those known previously. A proof of the optimality of the indicated moments is based on combinatorial analysis of random walk trajectories.

*Key words*:
symmetric random walk, optimal stopping, "Buy-and-hold" rule.