Refereed journal article or data article (A1)

Optimal variance stopping with linear diffusions




List of Authors: Kamille Sofie Tågholt Gad, Pekka Matomäki

Publisher: Elsevier

Publication year: 2020

Journal: Stochastic Processes and their Applications

Journal name in source: Stochastic Processes and their Applications

Volume number: 130

ISSN: 0304-4149

eISSN: 1879-209X

DOI: http://dx.doi.org/10.1016/j.spa.2019.07.001

URL: https://doi.org/10.1016/j.spa.2019.07.001

Self-archived copy’s web address: https://arxiv.org/abs/1612.09167


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.


Last updated on 2022-23-02 at 13:53