A knowledge of measure-theoretic probability theory (as taught e.g. in the course 401-3601-00L Probability Theory) is required.
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 an overview of courses offered in the area of mathematical finance, see link.
Lecture notes covering the material addressed during the lectures, as well as the content from the aforementioned prerequisites will be made available to the students through Polybox (you will receive a link and a password when the semester starts). Please note that the content of the notes often goes beyond that of the lectures, though only the material covered in class and during the exercise sessions is exigible. The notes will also be updated throughout the semester.
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. We prove the fundamental theorem of asset pricing and the hedging duality theorems, and also study convex duality in utility maximisation.
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.
Lectures are for a great majority scheduled to be in-person. A few lectures during the semester may be either via Zoom or pre-recorded, but you will be notified in advance when this happens. Recordings for the 2021 lectures will also be systematically provided for your convenience, though they may differ a bit from the material actually covered during the in-person lectures.
The assistants of Group 3 (Probability Theory, Insurance Mathematics and Stochastic Finance) offer regular office hours for questions on courses and exercise classes taught by the professors in the group. Click here for more information.
Exercise classes take place every Thursday in HG E 33.1 and will be in person for a great majority. A few exercise sessions during the semester may be via Zoom and you will be notified in advance when this happens. Even though it is not obligatory, you are encouraged to solve the exercises and submit your solutions since similar assignments may be a part of the exam. Should you decide to do so, please hand in your solutions in Daniel Kršek's box near the door to HG G 53.2. Submission by email as a PDF file is also possible. Your solutions have to be submitted before 18:00 of the corresponding due date (typically on Monday). They will then be corrected and returned during the following exercise class or returned to the box if not collected (or sent by email if submitted by email).
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