Abstract
We consider a class of optimal stopping problems involving both the running maximum as well as the prevailing state of a linear diffusion. Instead of tackling the problem directly via the standard free boundary approach, we take an alternative route and present a parameterized family of standard stopping problems of the underlying diffusion. We apply this family to delineate circumstances under which the original problem admits a unique, well-defined solution. We then develop a discretized approach resulting in a numerical algorithm for solving the considered class of stopping problems. We illustrate the use of the algorithm in both a geometric Brownian motion and a mean reverting diffusion setting.
Citation
Luis H. R. Alvarez. Pekka Matomäki. "Optimal stopping of the maximum process." J. Appl. Probab. 51 (3) 818 - 836, September 2014. https://doi.org/10.1239/jap/1409932676
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