On an Effective Solution of the Optimal Stopping Problem for Random Walks

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

No 131, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

Abstract: 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.

Keywords: optimal stopping; random walk; rate of convergence; Appell polynomials (search for similar items in EconPapers)
Pages: 13 pages
Date: 2004-08-01
New Economics Papers: this item is included in nep-ets
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Citations: View citations in EconPapers (8)

Published as: Novikov, A. and Shiryaev, A., 2006, "On an Effective Solution of the Optimal Stopping Problem for Random Walks", Theory of Probability and Its Applications, 49(2), 344-354.

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