Bergische Universität Wuppertal
Fachbereich Mathematik und Naturwissenschaften
Angewandte Mathematik - Numerische Analysis (AMNA)


Prof. Dr. Matthias Ehrhardt
Prof. Dr. Michael Günther
PD Dr. Jörg Kienitz

Lecture Summer Term 2020:

Mathematical Foundations of Machine Learning with Applications in Finance
(Advanced Topic)

(Start of Lecture ??.04.20)

Adressen und Termine
(Beginn der VL 07.04., Beginn der UE 12.04)
 Vorlesung   Mo,  10:15 - 11:45   Hörsaal ?? 
   Mo,  12:15 - 13:45   Hörsaal ??  

Outline of the Lecture

The lecture is suitable for students of mathematics as well as for economics.
The students of economathematics can use it as component AKap.NAaA-a "Selected Topics in Numerical Analysis and Algorithms" in the module of the same name.

Topics of the Lecture:
The aim of the lecture is to introduce the mathematical concepts underlying the theory of approximating a function using machine learning, resp. to be more precise deep learning methods. To this end we give an introduction to the theory and show how this can be used for exploring Neural Networks. To illustrate the applicability of Neural Networks in Finance we consider the pricing of derivatives and the calibration of parametric models. For pricing we consider the Black-Scholes-Merton, the Hull-White and the Heston model. Calibration is considered for the Black-Scholes-Merton and the Heston model.

Outline of the lecture:

  1. Introduction to Learning Theory
  2. Pricing Financial Derivatives
  3. Neural Networks
detailed outline of the lecture.


Previous knowledge: Analysis I - III, basic knowledge of ordinary differential equations, stochastics.

For the exercises we recommend to install the Python distribution from Anaconda and install the packages tensorflow, keras, pytorch, matplotlib. If other packages are necessary these can easily installed on demand.

Criteria: Regular participation and participation in the exercise groups, as well as reaching 50% of the possible points on the first seven or the remaining exercise sheets and at least 2/3 of the possible points for the practical tasks.

University of Wuppertal
Faculty of Mathematics and Natural Sciences
Department of Mathematics
Applied Mathematics & Numerical Analysis Group

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