This course gives an introduction to Brownian motion and stochastic calculus. It includes the construction and properties of Brownian motion, basics of Markov processes in continuous time and of Levy processes, and stochastic calculus for continuous semimartingales.

This course covers some basic objects of stochastic analysis. In particular, the following topics are discussed: construction and properties of Brownian motion, stochastic integration, Ito's formula and applications, stochastic differential equations and connection with partial differential equations.

Introductory course on mathematics for investment, hedging, portfolio management, asset pricing and financial derivatives in discrete-time financial markets. Topics: arbitrage, completeness, risk-neutral pricing, utility maximisation, and maybe others. Fundamental theorem of asset pricing, hedging duality theorems in discrete time, convex duality in utility maximisation.

Advanced course on mathematical finance:- semimartingales and general stochastic integration- absence of arbitrage and martingale measures- fundamental theorem of asset pricing- option pricing and hedging- hedging duality- optimal investment problems- additional topics

Advanced course on mathematical finance:- semimartingales and general stochastic integration- absence of arbitrage and martingale measures- fundamental theorem of asset pricing- option pricing and hedging- hedging duality- optimal investment problems- additional topics

First introduction to main modelling ideas and mathematical tools from mathematical finance

Basics of probability theory and the theory of stochastic processes in discrete time

Introduction to probability and statistics

Probability and Statistics

Introduction to probability theory and statistics

- Diskrete Wahrscheinlichkeitsräume- Stetige Modelle- Grenzwertsätze- Einführung in die Statistik

Basic concepts from probability and statistics:- introduction to probability theory- short introduction to basic concepts and methods from statistics

The goal of this seminar is to present various stochastic methods for claims reserving.These methods enable to set adequate reserves for open claims and todetermine prediction errors of these estimators.

This lecture covers the mathematical modelling of interest-rate and credit risks and the application of quantitative models to the pricing of interest-rate and credit derivatives.