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Optimal variance stopping with linear diffusions

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  • Gad, Kamille Sofie Tågholt
  • Matomäki, Pekka

Abstract

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.

Suggested Citation

  • Gad, Kamille Sofie Tågholt & Matomäki, Pekka, 2020. "Optimal variance stopping with linear diffusions," Stochastic Processes and their Applications, Elsevier, vol. 130(4), pages 2349-2383.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:4:p:2349-2383
    DOI: 10.1016/j.spa.2019.07.001
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    References listed on IDEAS

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    1. Yu-Jui Huang & Adrien Nguyen-Huu, 2018. "Time-consistent stopping under decreasing impatience," Finance and Stochastics, Springer, vol. 22(1), pages 69-95, January.
    2. Yu-Jui Huang & Zhou Zhou, 2017. "Optimal Equilibria for Time-Inconsistent Stopping Problems in Continuous Time," Papers 1712.07806, arXiv.org, revised Oct 2018.
    3. Yu-Jui Huang & Zhou Zhou, 2017. "The Optimal Equilibrium for Time-Inconsistent Stopping Problems -- the Discrete-Time Case," Papers 1707.04981, arXiv.org, revised Dec 2018.
    4. Touzi, N. & Vieille, N., 1999. "Continuous-Time Dynkin Games with Mixed Strategies," Papiers d'Economie Mathématique et Applications 1999.112, Université Panthéon-Sorbonne (Paris 1).
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