Optimal variance stopping with linear diffusions

Research output: Contribution to journalJournal articlepeer-review

  • Kamille Sofie Tågholt Gad
  • Pekka Matomäki

We study the optimal stopping problem of maximizing the variance of an unkilled linear diffusion. Especially, we demonstrate how the problem can be solved as a convex two-player zero-sum game, and reveal quite surprising application of game theory by doing so. Our main result shows that an optimal solution can, in a general case, be found among stopping times that are mixtures of two hitting times. This and other revealed phenomena together with suggested solution methods could be helpful when facing more complex non-linear optimal stopping problems. The results are illustrated by a few examples.

Original languageEnglish
JournalStochastic Processes and Their Applications
Volume130
Issue number4
Pages (from-to)2349-2383
ISSN0304-4149
DOIs
Publication statusPublished - 2020

Bibliographical note

Publisher Copyright:
© 2019 Elsevier B.V.

    Research areas

  • Infinite zero-sum game, Linear diffusion, Non-linear optimal stopping, Optimal stopping, Variance

Links

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