Date of Award

May 2017

Degree Type


Degree Name

Master of Science



First Advisor

Chao Zhu

Committee Members

Richard Stockbridge, Jay Beder


Geometric Brownian Motion, Mean Reversion Trading, Optimal Stopping, Perpetual Put


This thesis is focused on the perpetual American put option under the geometric Brownian motion and mean-reverting models. Two approaches, which have been applied before to the call option of a mean-reverting process, will be studied in details for the two models. The first approach amounts to solving the associated quasi-variational inequality for the optimal stopping problem. A verification theorem is proved to demonstrate that the solution to the quasi-variational inequality agrees with the value function. The second approach is based on detailed analyses of an auxiliary two-point stopping problem, which leads to an explicit expression for the value function. Both approaches identify an optimal execution rule for the two models.

Included in

Mathematics Commons