## Autumn Semester 2020

- Mathematik I
Mathematics I / II is an introductory lecture to one-dimensional and multidimensional analysis and linear algebra with a special emphasis on applications in natural sciences. The course is taught in German.

## Spring Semester 2020

- Introduction to Mathematical Finance
This is an introductory course on the mathematics for investment, hedging, portfolio management, asset pricing and financial derivatives in discrete-time financial markets. We discuss arbitrage, completeness, risk-neutral pricing and utility maximisation. We prove the fundamental theorem of asset pricing and the hedging duality theorems, and also study convex duality in utility maximization.

- Supervision of bachelor project on efficient calibration of stochastic financial models using deep learning.

## Autumn Semester 2019

- Mathematical Foundations for Finance
This course gives a first introduction to the main modelling ideas and mathematical tools from mathematical finance. It mainly aims at non-mathematicians who need an introduction to the main tools from stochastics used in mathematical finance. However, mathematicians who want to learn some basic modelling ideas and concepts for quantitative finance (before continuing with a more advanced course) may also find this of interest. The main emphasis will be on ideas, but important results will be given with (sometimes partial) proofs.

Topics to be covered include

- financial market models in finite discrete time
- absence of arbitrage and martingale measures
- valuation and hedging in complete markets
- basics about Brownian motion
- stochastic integration
- stochastic calculus: Itô's formula, Girsanov transformation, Itô's martingale representation theorem
- Black-Scholes model

If time permits, I would like to include a brief digression on

- limitations of the Black-Scholes model and potential extensions: local volatility and stochastic volatility models, model calibration (implied vol-surface), jump diffusion models, rough stochastic volatility models, ....
- applications of Machine Learning in finance: deep hedging, deep portfolio optimization, deep model calibration, ...