Probability and Measure

**This information is for the 2019/20 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. Martingales. Stochastic processes. Brownian motion. The Itô integral.

**Teaching**

20 hours of lectures and 10 hours of seminars in the MT. 1 hour of lectures in the ST.

The lecture in the Summer Term is a Revision Lecture.

**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 summer exam period.

**
Key facts
**

Department: Mathematics

Total students 2018/19: 20

Average class size 2018/19: 21

Controlled access 2018/19: No

Value: Half Unit

**Personal development skills**

- Self-management
- Problem solving
- Application of information skills
- Communication
- Application of numeracy skills
- Specialist skills