On an effective solution of the optimal stopping problem for random walks

Publication Type:
Journal Article
Theory of Probability and its Applications, 2005, 49 (2), pp. 344 - 354
Issue Date:
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We find a solution of the optimal stopping problem for the case when a reward function is an integer power function of a random walk on an infinite time interval. It is shown that an optimal stopping time is a first crossing time through a level defined as the largest root of Appell's polynomial associated with the maximum of the random walk. It is also shown that a value function of the optimal stopping problem on the finite interval {0, 1, . . . , T} converges with an exponential rate as T → ∞ to the limit under the assumption that jumps of the random walk are exponentially bounded.
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