Mathematics for New Technologies in Finance Spring 2024

Lecturer
Prof. Dr. Josef Teichmann
Coordinator
Tengyingzi (Sophia) Perrin

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 adversersial networks, Economic games.

Prerequisites

Bachelor in mathematics, physics, economics or computer science.

Lectures

  • Lectures take place on Mon 10:15-12:00 at HG G 5 and Wed 11:15-12:00 at HG G5.
  • Lectures and classes will not take place during Easter week from Friday, 29.03.2024 to Sunday, 07.04.2024.
  • Lecture Notes

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

    Exercises

    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 class Exercise sheet References
    Wed 21 Feb. Exercise sheet 1
    Exercise notebook 1
    Solution sheet 1
    Solution notebook 1
    The Faber–Schauder system
    G. Cybenko's proof
    Kurt Hornik and Shimon Schocken's proof
    Moshe Leshno, etc.'s proof
    Wed 28 Feb. Exercise sheet 2
    Solution sheet 2
    Interpolation and approximation by polynomials (Chapter 6)
    Lebesgue's Proof of Weierstrass' Theorem
    A theoretical framework for backpropagation
    Wed 6 Mar(Only in HG E21) Exercise sheet 3
    Solution sheet 3
    Differential equations driven by rough paths
    Neural ordinary differential equations
    Wed 13 Mar(Only in HG E21) Exercise sheet 4
    Solution sheet 4
    Neural Controlled Differential Equations for Irregular Time Series
    Wed 20 Mar(Only in HG E21) Exercise sheet 5
    Exercise notebook 5
    Solution sheet 5
    Solution notebook 5
    Deep Hedging
    PFhedge
    Wed 27 Mar(Only in HG E21) Sample project 1 (Yahang Qi)
    Sample project 2 (Julian Pachschwoell)
    Wed 10 Apr(Only in HG E21) Exercise sheet 6
    Solution sheet 6
    Bayesian-interpretation-of-ridge-regression
    Wed 17 Apr(Only in HG E21) Exercise sheet 7
    Solution sheet 7
    Solution notebook 7
    Calibration of Local Stochastic Volatility Models to Market Smiles: A Monte Carlo Approach
    Local Volatility and Dupire's Equation
    Wed 24 Apr(Only in HG E21) Robust Utility Optimization: A GAN approach

    Literature