Mathematics for New Technologies in Finance Spring 2025

Lecturer
Prof. Dr. Josef Teichmann , Prof. Dr. Philipp Harms
Coordinator
Filippo Beretta

Content

This course will deal with the following topics with rigorous proofs and many coding excursions: Universal approximation theorems, Stochastic gradient Descent, Deep networks and wavelet analysis, Deep Hedging, Deep calibration, Different network architectures, Reservoir Computing, Time series analysis by machine learning, Reinforcement learning, generative adversarial networks, Economic games, Large Language Models in Finance.

Prerequisites

Bachelor in mathematics, physics, economics or computer science.

Lectures

Lectures take place on Wed 10:15-13:00 at HG G 3 .

Lectures and classes will not take place during Easter week from Friday, 18.04.2025 to Sunday, 27.04.2025.

Lecture Notes

Lecture notes are provided as ipython notebooks or in form of slides as well as of classical notes.

Office hours

The assistants of Group 3 (Probability Theory, Insurance Mathematics and Stochastic Finance) offer regular office hours for questions on courses and exercise classes taught by the professors in the group.

During the semester, the assistant hours take place Mondays and Thursdays, 12:00–13:00, in room HG G 32.6. The regular assistant hours start in the fourth week of the semester. Click here for more information.

Exercise classes

Exercises will be available in the exercise class. Students are expected to voluntarily do calculations and present results in class. Solutions will also be released right during the exercise class.

Exercise classes take place on Mon 13:15-14:00 at HG D 3.2.

Exercise classExercise sheetReferences
Mon 17 Feb.
(No class)
Introduction to NumPy and Matplotlib
Introduction to TensorFlow and Keras
Introduction to Pytorch
Scientific Python lecture notes
Keras blog
Pytorch tutorials
Mon 24 Feb.
Exercise sheet 1
Exercise notebook 1.1
Exercise notebook 1.2
Solution sheet 1
Solution notebook 1.1
Solution notebook 1.2
The Faber–Schauder system
G. Cybenko's proof
Kurt Hornik and Shimon Schocken's proof
Moshe Leshno, etc.'s proof
Mon 3 Mar.
Exercise sheet 2
Exercise notebook 2.1
Solution sheet 2
Solution notebook 2.1
Interpolation and approximation by polynomials (Chapter 6)
Lebesgue's Proof of Weierstrass' Theorem
Mon 10 Mar.
Exercise sheet 3
Differential equations driven by rough paths
Neural ordinary differential equations

Literature