Optimal Stopping for Absolute Maximum of Homogeneous Diffusion / A. A. Kamenov. // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2015. № 5. P. 7-13 [Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 202-207].
The optimal stopping problem is studied in the paper for functions dependent on the absolute maximum of some homogeneous diffusion. The cases of infinite and finite time horizons are considered. A differential equation for the optimal stopping boundary is obtained in both the cases. A principle of maximum is proved for a function satisfying a single-crossing condition.
Key words: homogeneous diffusions, optimal stopping, maximum process, envelope theorem.