Occurrence | Teaching period |
---|---|
A1 | Semester 1 2024-25 |
A2 | Semester 1 2024-25 to Semester 2 2024-25 |
B1 | Semester 2 2024-25 |
B2 | Semester 2 2024-25 to Semester 1 2025-26 |
This module provides the mathematical foundations underpinning Mathematical Finance. The topics covered are selected because of their importance in quantitative finance theory and practice. Probability theory and stochastic processes provide the language in which to express and solve mathematical problems in finance due to the inherent randomness of asset prices. The introduction of more advanced tools will be preceded by a brief review of basic probability theory with particular focus on conditional expectation. Then the module will proceed to present the theory of martingales and the study of three basic stochastic processes in finance: random walks, Brownian motion, and the Poisson process. An informal overview of Ito stochastic calculus will be given and first financial applications indicated. The material will be illustrated by numerous examples and computer-generated demonstrations. By the end of this module students are expected to achieve a sufficient level of competence in selected mathematical methods and techniques to facilitate further study of Mathematical Finance.
By the end of this module students should
Task | % of module mark |
---|---|
Coursework - extensions not feasible/practicable | 100 |
Oral presentation/seminar/exam | 0 |
None
Task | % of module mark |
---|---|
Coursework - extensions not feasible/practicable | 100 |
Oral presentation/seminar/exam | 0 |
Information currently unavailable
1. M. Capinski and E. Kopp, Measure, Integral and Probability, 2nd edition, Springer 2007.
2. E. Kopp, J. Malczak and T. Zastawniak, Probability for Finance, Cambridge University Press 2014 (to appear).
3. M. Capinski and T. Zastawniak, Probability Through Problems, Springer 2001.
4. M. Capinski and T. Zastawniak, Mathematics for Finance: An Introduction to Financial Engineering, Springer 2003.
5. Z. Brzezniak and T. Zastawniak, Basic Stochastic Processes, Springer 1999