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, various aspects of probability theory are considered. The first part covers the main theorems in the field (law of large numbers, central limit theorem), while the second part focuses on the theory of martingales and concentration inequalit ...
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. ...
This course will provide a basic knowledge of the stochastic calculus of variations with respect to the Brownian motion. A variety of applications will be presented including the regularity of probability densities and quantitative normal approximations. ...
The aim of the course is to apply the theory of martingales in the context of mathematical finance. The course provides a detailed study of the mathematical ideas that are used in modern financial mathematics. Moreover, the concepts of complete and incompl ...