401-3888-00L  Introduction to Mathematical Finance

SemesterSpring Semester 2017
LecturersJ. Teichmann
Periodicityyearly recurring course
Language of instructionEnglish
CommentA 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.


AbstractThis 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. We prove the fundamental theorem of asset pricing and the hedging duality theorems, and also study convex duality in utility maximization.
ObjectiveThis 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 also study convex duality in utility maximization.
ContentThis course focuses on discrete-time financial markets and presumes a knowledge of measure-theoretic probability theory (as taught e.g. in the course "Probability Theory"). The course will be offered every year in the Spring semester. The textbook by Föllmer and Schied or lecture notes similar to that will be used.

This course is the first of a sequence of two courses on mathematical finance. The second course "Mathematical Finance" (MFII), 401-4889-00, focuses on continuous-time models. It is advisable that the present course, MFI, is taken prior to MFII.
Lecture notesThe textbook by Föllmer and Schied or lecture notes similar to that will be used. However, actual lecture notes will not be available.
LiteratureRecommended textbook:

Hans Föllmer and Alexander Schied, "Stochastic Finance: An Introduction in Discrete Time", de Gruyter
Prerequisites / NoticeA related course is "Mathematical Foundations for Finance" (MFF), 401-3913-01. Although both courses can be taken independently of each other, only one will be given credit points for the Bachelor and the Master degree. In other words, it is also not possible to earn credit points with one for the Bachelor and with the other for the Master degree.

This course is the first of a sequence of two courses on mathematical finance. The second course "Mathematical Finance" (MFII), 401-4889-00, focuses on continuous-time models. It is advisable that the present course, MFI, is taken prior to MFII.