Optimal stopping problems as free boundary problems and applications to finance

In this project, we present a methodology to transform Optimal Stopping Problems into Free Boundary Problems. The theory of Optimal Stopping can be found in fields such as statistics, theory of probability and mathematical finance. First of all, we include all the necessary concepts in order to understand this strategy, from the most basic definitions such as stochastic processes and Brownian motion to the most sophisticated results such as Dynkin's formula and the High Contact Principle. We also give three interesting applications, two of them from the area of mathematical finance. The third one is the most elaborated and it is about predicting resistance and support levels of an asset price. In this one, we also give an algorithm to calculate numerically the solution of the problem: the optimal stopping boundary