Upon successful completion of this course, students will:

* Understand and use basic structures and results in stochastic processes in discrete and continuous time, including Brownian motion, martingales, stopping times, changes of measure, stochastic integrals, and Itô’s formula.

* Understand the connection between no-arbitrage, market completeness, and risk-neutral measures in the context of discrete-time models and the Black-Scholes model.

* Apply risk-neutral pricing and hedging techniques to standard European and American options in both discrete-time models and the Black-Scholes model.

* Understand and use the connection between option pricing and partial differential equations (PDEs).

* Demonstrate a basic understanding of optimal stopping problems and their solutions in the context of pricing American options in discrete-time models and the Black-Scholes model.