MA411      Half Unit
Probability and Measure

This information is for the 2024/25 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 Autumn 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 2023/24: 12

Average class size 2023/24: 12

Controlled access 2023/24: No

Value: Half Unit

Guidelines for interpreting course guide information

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