Geodesic
On an effective solution of the optimal
Teoriâ veroâtnostej i ee primeneniâ, Tome 49 (2004) no. 2, pp. 373-382

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{TVP_2004_49_2_a10,
     author = {A. A. Novikov and A. N. Shiryaev},
     title = {On an effective solution of the optimal},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {373--382},
     publisher = {mathdoc},
     volume = {49},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2004_49_2_a10/}
}
TY  - JOUR
AU  - A. A. Novikov
AU  - A. N. Shiryaev
TI  - On an effective solution of the optimal
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2004
SP  - 373
EP  - 382
VL  - 49
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2004_49_2_a10/
LA  - ru
ID  - TVP_2004_49_2_a10
ER  - 
%0 Journal Article
%A A. A. Novikov
%A A. N. Shiryaev
%T On an effective solution of the optimal
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2004
%P 373-382
%V 49
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2004_49_2_a10/
%G ru
%F TVP_2004_49_2_a10
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/