MA411 Half Unit
Probability and Measure
This information is for the 2023/24 session.
Teacher responsible
Dr Pavel Gapeev
Availability
This course is available on the MSc in Applicable Mathematics, MSc in Financial Mathematics and MSc in Quantitative Methods for Risk Management. This course is available as an outside option to students on other programmes where regulations permit.
Pre-requisites
Some background in real analysis is essential.
Course content
The purposes of this course are (a) to explain the formal basis of abstract probability theory, and the justification for basic results in the theory, and (b) to explore those aspects of the theory most used in advanced analytical models in economics and finance. The approach taken will be formal. Probability spaces and probability measures. Random variables. Expectation and integration. Convergence of random variables. Conditional expectation. The Radon-Nikodym Theorem. Bayes' formula. Martingales. Stochastic processes. Brownian motion. The Itô integral.
Teaching
This course is delivered through a combination of classes and lectures totalling a minimum of 30 hours across Michaelmas Term.
Formative coursework
Written answers to set problems will be expected on a weekly basis.
Indicative reading
Full lecture notes will be provided. The following may prove useful: J S Rosenthal, A First Look at Rigorous Probability Theory; G R Grimmett & D R Stirzaker, Probability and Random Processes; D Williams, Probability with Martingales; M Caplinski & E Kopp, Measure, Integral and Probability; J Jacod & P Protter, Probability Essentials.
Assessment
Exam (100%, duration: 2 hours) in the spring exam period.
Key facts
Department: Mathematics
Total students 2022/23: 14
Average class size 2022/23: 14
Controlled access 2022/23: No
Lecture capture used 2022/23: Yes (MT)
Value: Half Unit
Course selection videos
Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.
Personal development skills
- Self-management
- Problem solving
- Application of information skills
- Communication
- Application of numeracy skills
- Specialist skills