In this seminar we provide an introduction to stochastic integration with respect to semimartingales. We start by recalling some basic knowledge concerning the theory of stochastic processes, including elementary martingale theory. We give then the definition of stochastic integral and study its properties. In particular we consider:
1. Local martingales.
2. Introduction to semimartingales.
3. Definition of stochastic integral with respect to semimartingales.
4. Itô’s formula.
5. Girsanov’s Theorem.
6. Stochastic integration for predictable integrands.