Financial Mathematics

The aim of the course is to introduce the students to the probabilistic study of the classical theory of mathematical finance.

The first part of the course is centered around stochastic calculus. In this first part, we introduce a detailed theory of stochastic integration that will be the basis for the second part of the course (which will be more financial and rely on the mathematical theory as studied on the first part).

In the second part of the course, we will then cover arbitrage theory, perfect markets, risk-neutral pricing of options and other derivatives, Black-Scholes-Merton model, models for exchange rates and interest rates.

For each topic and model we will stress its points of strength, but also its points of weakness.