Optimal variance stopping with linear diffusions

Kamille Sofie Tågholt Gad, Pekka Matomäki

Published 2016-12-29Version 1

We study the optimal stopping problem of maximizing the variance of an unkilled linear diffusion. Especially, we reveal its close connection to game theory. Our main result shows that an optimal solution can often 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.