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

Siam Publications
Publication Type:
Journal Article
Theory of Probability and its Applications, 2005, 49 (2), pp. 344 - 354
Issue Date:
Full metadata record
Files in This Item:
Filename Description SizeFormat
2005003710.pdf974 kBAdobe PDF
We find a solution of the optimal stopping problem for the case when a reward function is an integer 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 approaches infinity to the limit under the assumption that jumps of the random walk are exponentially bounded
Please use this identifier to cite or link to this item: