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1 results

  • Optimal Stopping of the Maximum Process

  • Part of
  • Luis H. R. Alvarez, Pekka Matomäki
  • Journal:
    Journal of Applied Probability / Volume 51 / Issue 3 / September 2014
    Published online by Cambridge University Press:
    30 January 2018, pp. 818-836
    Print publication:
    September 2014
    • Article
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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.