Geodesic
The optimal stopping problem concerned with ultimate maximum of a L\'evy process
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2011), pp. 22-27

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For a Lévy process $X=(X_{t})_{0\le t\infty}$ we consider the moment $\theta=\inf\{t\ge 0\colon\sup_{s\le t} X_{s}=\sup_{s\ge 0}X_{s}\}$. We study an optimal approximation of the moment $\theta$ using the information available at the moment. As an example we consider a Lévy process which is a combination of a Brownian motion with a drift and a Poisson process. 
@article{VMUMM_2011_4_a3,
     author = {S. S. Sinelnikov},
     title = {The optimal stopping problem concerned with ultimate maximum of a {L\'evy} process},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {22--27},
     publisher = {mathdoc},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2011_4_a3/}
}
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S. S. Sinelnikov. The optimal stopping problem concerned with ultimate maximum of a L\'evy process. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2011), pp. 22-27. http://geodesic.mathdoc.fr/item/VMUMM_2011_4_a3/