Journal of Applied Probability

Optimal stopping of the maximum process

Luis H. R. Alvarez and Pekka Matomäki

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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.

Article information

J. Appl. Probab., Volume 51, Number 3 (2014), 818-836.

First available in Project Euclid: 5 September 2014

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60J60: Diffusion processes [See also 58J65] 62L15: Optimal stopping [See also 60G40, 91A60]
Secondary: 60G40: Stopping times; optimal stopping problems; gambling theory [See also 62L15, 91A60]

Optimal stopping linear diffusions maximum process


Alvarez, Luis H. R.; Matomäki, Pekka. Optimal stopping of the maximum process. J. Appl. Probab. 51 (2014), no. 3, 818--836. doi:10.1239/jap/1409932676.

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