Oscar Fredrik Olof Sjöstrand: Optimal Stopping in American Put Options: A Mathematical Analysis

Abstract.

In this thesis, we explore the mathematical results used to find a solution to the optimal stopping problem for American put options. We begin with an overview of probability theory, stochastic processes, and stochastic calculus to build a foundation for understanding the optimal stopping problem. We then apply these mathematical concepts to derive and prove a solution for the perpetual American put option. Additionally, we analyze the reasonableness of our results in the context of the characteristics of the underlying asset on which the option is based.