Abstract:
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 {O, 1, ... ,T} converges with an exponential
rate as T ---t 00 to the limit under the assumption that jumps of the random walk are exponentially
bounded.
