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 ...
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 ...
In this course we will introduce and study numerical integrators for stochastic differential equations. These numerical methods are important for many applications. ...
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. ...
This class is an introduction to Machine Learning and High Dimensional Statistics in Finance. We start with purely empirical approach, focusing first on high dimensional regressions then moving to kernel methods and deep learning, and then study equilibriu ...
Biology is becoming more and more a data science, as illustrated by the explosion of available genome sequences. This course aims to show how we can make sense of such data and harness it in order to understand biological processes in a quantitative way. ...
Supersymmetry is the unique quantum extension of the symmetry principles of relativity.
This course offers a first but broad introduction covering the role of Supersymmetry in our understanding of both physics beyond the Standard Model and non-perturbative ...