In this lecture series we will discuss two important topics in math finance: option pricing and optimal asset allocation.

In the first part, we will introduce the Black-Scholes theory for pricing financial derivatives. In the second part, asset alocation will be discussed using the optimal control framework developed by Merton. Most of the discussions are based on continuous time even though numerical issues will be addressed as well. The aim of the lecture series is to give the students a short and gental introduction to two of the most important subjects in modern finance.