# SF2971 - Martingales and Stochastic Integrals (KTH Stockholm)

## Introduction

### Course contents

- Conditional expectation, martingales and stochastic integrals in discrete time, stopping times, Girsanov Theorem.
- Martingales in continuous time, Brownian motion, Ito integral and Ito Lemma.
- Martingale representation Theorem, Stochastic Differential Equations (SDEs), Ito diffusions, Kolmogorov equations, Feynman-Kac formula, stopping times and optional stopping.

### Intended learning outcomes

After passing the course, the students should be able to

- Formulate and explain central definitions and theorems within the theory of martingales and stochastic integrals;
- Solve basic problems within the theory of martingales and stochastic integrals, and apply its methods to stochastic processes.