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. 72, N 2, 2017. P. 0].

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.

№ 4/2011