On a solution of the optimal stopping problem for processes with independent increments

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Journal Article
Stochastics, 2007, 79 (3-4), pp. 393 - 406
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We discuss a solution of the optimal stopping problem for the case when a reward function is a power function of a process with independent stationary increments (random walks or Levy processes) on an infinite time interval. It is shown that an optimal stopping time is the first crossing time through a level defined as the largest root of the Appell function associated with the maximum of the underlying process.
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