Abstract:
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.
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