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The Optimal Stopping Problem Concerned with Ultimate Maximum of a Levy Process / Sinelnikov S.S. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2011. № 4. P. 22-27 [Moscow Univ. Math. Bulletin. Vol. 66, N 4, 2011.]. For a Levy process X = (Xt)0≤t<∞ we consider the time θ = inf {t ≥ 0: sups ≤ t Xs = sups ≥ 0 Xs}. We study an optimal approximation of the time θ using the information available at the current instant. A Levy process being a combination of a Brownian motion with a drift and a Poisson process is considered as an example.
Key words: moment of ultimate maximum, optimal stopping problem, Levy process,
Stefan problem.
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