Mathematics for New Technologies in Finance Spring 2023

Prof. Dr. Josef Teichmann
Songyan Hou


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 adversersial networks, Economic games.


Bachelor in mathematics, physics, economics or computer science.


Lectures take place on Mon 10:15-12:00 at HG G 5 and Wed 11:15-12:00 at HG F 5 .

Lectures and classes will not take place during Easter week from Friday, 07.04.2023 to Sunday, 16.04.2023.

Recordings of the lectures are available here .

Lecture Notes

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

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 Wed 10:15-11:00 at HG E 21 and LEE D 101.

Exercise classExercise sheetReferences
Wed 22 Feb.
(Lecture at only HG E 21)
Wed 01 March.
(Only in LEE D 101)
Exercise sheet 1
Exercise notebook 1
quick pytorch introduction
Solution sheet 1
Solution code 1
The Faber–Schauder system
G. Cybenko's proof
Kurt Hornik and Shimon Schocken's proof
Moshe Leshno, etc.'s proof
Wed 8 Mar. Exercise sheet 2
Solution sheet 2
Differential equations driven by rough paths
Wed 15 Mar. Exercise sheet 3
Solution sheet 3
Neural ordinary differential equations
A theoretical framework for backpropagation
How backpropagation works
Wed 16 Mar. Exercise sheet 4
Solution sheet 4
Malliavin Calculus: Analysis on Gaussian spaces
Wed 29 Mar. Exercise notebook 5 Deep Hedging
Wed 5 April. Exercise notebook 6 Stochastic Finance: An Introduction in Discrete Time
Wed 12 April. (Easter Break)
Wed 19 April. Exercise sheet 7
Solution sheet 7
Wed 26 April. Exercise sheet 8
Solution sheet 8
Calibration of local stochastic volatility models to market smiles: A monte-carlo approach
Wed 3 May.
(Lecture at only HG E 21)
Wed 10 May. Exercise sheet 9
Solution sheet 9
Differential equations driven by rough paths
Wed 16 May. Exercise sheet 10 Discrete-time signatures and randomness in reservoir computing
Wed 24 May. Exam 2023.02.09