Geodesic
On an effective solution of the optimal
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 2, pp. 373-382 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $\{0,1\ldots T\}$ converges with an exponential rate as $T\to\infty$ to the limit under the assumption that jumps of the random walk are exponentially bounded.
Keywords: optimal stopping, random walk, rate of convergence
Mots-clés : Appell polynomials. 
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A. A. Novikov; A. N. Shiryaev. On an effective solution of the optimal. Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 2, pp. 373-382. http://geodesic.mathdoc.fr/item/TVP_2004_49_2_a10/

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