On a Solution of the Optimal Stopping Problem for Processes with Independent Increments

Alexander Novikov and Albert Shiryaev
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Alexander Novikov: Department of Mathematics, University of Technology Sydney
Albert Shiryaev: Mathematical Institute, Moscow, Russia

No 178, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: 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.

Pages: 15 pages
Date: 2006-06-01
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Citations: View citations in EconPapers (6)

Published as: Novikov, A. and Shiryaev, A, 2007, "On a Solution of the Optimal Stopping Problem for Processes with Independent Increments", Stochastics An International Journal of Probability and Stochastic Processes, 79(3-4), 393-406.

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