Geodesic
Degeneracy condition for the optimal moment in the optimal stopping problem for a new functional of a symmetric random walk and its maximum
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2015), pp. 3-13

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New classes of functionals are proposed for an optimal stopping problem for a functional of a symmetric random walk and its maximum. For one class the optimal moment in a finite time interval is the beginning of this interval and for another one this is its end. These classes generalize those known previously. A proof of the optimality of the indicated moments is based on combinatorial analysis of random walk trajectories. 
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     author = {A. L. Vorob'ev},
     title = {Degeneracy condition for the optimal moment in the optimal stopping problem for a new functional of a symmetric random walk and its maximum},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {3--13},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2015_4_a0/}
}
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A. L. Vorob'ev. Degeneracy condition for the optimal moment in the optimal stopping problem for a new functional of a symmetric random walk and its maximum. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2015), pp. 3-13. http://geodesic.mathdoc.fr/item/VMUMM_2015_4_a0/