This course gives an introduction to probability theory and stochastic calculus in discrete and continuous time. The fundamental notions and techniques introduced in this course have many applications in finance, for example for option pricing, risk mana ...
This course introduces slow/fast systems and the mathematical tools used to derive effective equations governing their behaviour. Students will learn core concepts and techniques for rigorously analysing complex stochastic multi-scale systems. ...
Introduction to the mathematical theory of stochastic calculus: construction of the Ito stochastic integral, proof of the Ito formula, introduction to stochastic differential equations, Girsanov's theorem and the Feynman-Kac formula, the martingale represe ...
In this course we will introduce and study numerical integrators for stochastic differential equations. These numerical methods are important for many applications. ...