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1 results

  • Variance Optimal Stopping for Geometric Lévy Processes

  • Part of
  • Kamille Sofie Tågholt Gad, Jesper Lund Pedersen
  • Journal:
    Advances in Applied Probability / Volume 47 / Issue 1 / March 2015
    Published online by Cambridge University Press:
    04 January 2016, pp. 128-145
    Print publication:
    March 2015
    • Article
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  • The main result of this paper is the solution to the optimal stopping problem of maximizing the variance of a geometric Lévy process. We call this problem the variance problem. We show that, for some geometric Lévy processes, we achieve higher variances by allowing randomized stopping. Furthermore, for some geometric Lévy processes, the problem has a solution only if randomized stopping is allowed. When randomized stopping is allowed, we give a solution to the variance problem. We identify the Lévy processes for which the allowance of randomized stopping times increases the maximum variance. When it does, we also solve the variance problem without randomized stopping.