MA411      Half Unit
Probability and Measure

This information is for the 2013/14 session.

Teacher responsible

Dr Arne Lokka

Availability

This course is available on the MSc in Applicable Mathematics, MSc in Financial Mathematics and MSc in Risk and Stochastics. This course is available as an outside option to students on other programmes where regulations permit.

Pre-requisites

Some background in pure mathematics 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 9 hours of seminars in the MT. 1 hour of seminars in the LT.

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 main exam period.

Key facts

Department: Mathematics

Total students 2012/13: 23

Average class size 2012/13: 26

Value: Half Unit

Guidelines for interpreting course guide information

Personal development skills

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