News
Exam - please register by Wednesday, 4th FebruaryWritten on 29.01.26 by Frederik Herzberg As agreed in the lecture, the oral examinations (duration: 30 minutes) for our lecture course will be held on the following days:
Please register for the exam in LSF and also reserve your preferred exam date by sending a… Read more As agreed in the lecture, the oral examinations (duration: 30 minutes) for our lecture course will be held on the following days:
Please register for the exam in LSF and also reserve your preferred exam date by sending a short e-mail to herzberg@math.uni-sb.de (no later than 4 February 2026). The exam can be taken in either English or German. Wishing you all successful exams! |
Tutorial henceforth in seminar room 10 (E2 4, 316)Written on 17.11.25 (last change on 17.11.25) by Frederik Herzberg The tutorial will henceforth take place in Seminar Room 10 (building E2 4, room 316) -- at the usual time (Mondays 2:15-3:45pm), starting from today (17 November). |
Mathematical Finance
Prof. Dr. Frederik Herzberg
Contents
This lecture course covers the mathematical theory of financial markets in discrete time and will also introduce basic continuous-time interest rate models.
Topics include:
- Utility maximization in general one-period models; Capital Asset Pricing Model
- Arbitrage, hedging, option pricing and the fundamental theorems of asset pricing in general one-period models
- Multi-period models and self-financing portfolios
- The fundamental theorems of asset pricing in multi-period models
- The Cox-Ross-Rubinstein model and the Black-Scholes formula
- Interest-rate derivatives (e.g., forward-rate agreements, swaps, caps, swaptions)
- Short-rate models
Lectures
- Mondays, 12:15-1:45pm, Hörsaal IV (building E2 4, room 115)
- Thursdays, 12:15-1:45pm, Hörsaal IV (building E2 4, room 115)
The first lecture is scheduled for Monday, 13 October. There will be no lecture on Thursday, 16 October.
On Thursday, 11 December, the lecture will be held in Seminar Room 9 (building E2 4, room 319).
Tutorials
Mondays, 2:15-3:45pm, Seminar Room 10 (building E2 4, room 316)
Language
The course (both lectures and tutorials) will be taught in English, unless all participants agree on German. The oral exam can be taken in English or in German.
Recommended Prerequisites
- Stochastik I
- Stochastics II (offered in parallel this semester)
References
- Föllmer & Schied, Stochastic Finance, de Gruyter
- Brigo & Mercurio, Interest Models – Theory and Practice, Springer
- Evstigneev, Hens & Schenk-Hoppé, Mathematical Financial Economics, Springer
- Deutsch & Beinker, Derivate und interne Modelle, Schäffer und Poeschel
Course reference shelf, kindly provided by the Campus-Bibliothek für Informatik und Mathematik