Date of Award
Master of Science
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.
Siebigteroth, Ines Larissa, "Optimal Trading Under the American Perpetual Put Option for Geometric Brownian Motion and Mean-reverting Processes" (2017). Theses and Dissertations. 1540.