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401-3888-00L 9 Credits BSC , MSC D-ITET , D-MATH , D-INFK

Introduction to Mathematical Finance

Lecturers & Examiners: Prof. Dr. Beatrice Acciaio
A related course is 401-3913-01L Mathematical Foundations for Finance (3V+2U, 4 ECTS credits). Although both courses can be taken independently of each other, only one will be recognised for credits in the Bachelor and Master degree. In other words, it is not allowed to earn credit points with one for the Bachelor and with the other for the Master degree.
VVZ CR n/a

Last Updated: 2026-06-03 00:14:13

Abstract

Introductory course on mathematics for investment, hedging, portfolio management, asset pricing and financial derivatives in discrete-time financial markets. Topics: arbitrage, completeness, risk-neutral pricing, utility maximisation, and maybe others. Fundamental theorem of asset pricing, hedging duality theorems in discrete time, convex duality in utility maximisation.

Objective

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, and maybe other topics. We prove the fundamental theorem of asset pricing and the hedging duality theorems in discrete time, and we also study convex duality in utility maximization.

Content

This course focuses on discrete-time financial markets. It presumes a knowledge of measure-theoretic probability theory (as taught e.g. in the course "Probability Theory"). The course is offered every year in the Spring semester. This course is the first of a sequence of two courses on mathematical finance. The second course "Mathematical Finance" (MF II), 401-4889-00, focuses on continuous-time models. It is advisable that the present course, MF I, is taken prior to MF II. For a (not fully up-to-date) overview of courses offered in the area of mathematical finance, see Link .

Resources

Lecture Notes

The course is based on different parts from different textbooks as well as on original research literature. Lecture notes will not be available.

Literature

Literature: Michael U. Dothan, "Prices in Financial Markets", Oxford University Press Hans Föllmer and Alexander Schied, "Stochastic Finance: An Introduction in Discrete Time", de Gruyter Marek Capinski and Ekkehard Kopp, "Discrete Models of Financial Markets", Cambridge University Press Robert J. Elliott and P. Ekkehard Kopp, "Mathematics of Financial Markets", Springer Dmitry Kramkov and Walter Schachermayer, "The asymptotic elasticity of utility functions and optimal investment in incomplete markets", Annals of Applied Probability 9 (1999), 904-950

Learning Materials (Links)

General Information

Language
English
Levels
BSC , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
oral 30 minutes

Course Components

Type Title Time & Place Hours
lecture Introduction to Mathematical Finance
new schedule: tentatively Thu 12-14 and Fri 8-10
  • Thu 12:15-14:00 (HG E 1.1)
  • Fri 08:15-10:00 (ML E 12)
4 h weekly
exercise Introduction to Mathematical Finance
Groups are selected in myStudies. Thu 14-15 or Thu 15-16
  • Thu 14:15-15:00 (HG G 3)
  • Thu 15:15-16:00 (HG G 3)
1 h weekly

Offered In