The course is designed to provide students with an advanced knowledge of probability theory and stochastic calculus. It delivers the conceptual and analytical foundation used in other courses, such as Financial Derivatives and Modelling and Forecasting Financial Markets. Topics include sigma algebra, measure theory, probability spaces, stochastic processes in discrete and continuous time, Ito Calculus, martingales, random walks, Brownian motion, and their properties.

Ten weekly 2-hour lectures and nine weekly 1-hour tutorials.

A one-hour in-course examination (25% of final grade for course) and a two-hour end-of-course examination (75% of final grade for course).

ILO Assessment   Weighting Description (time/ word limit etc.)

1-3 In-course exam 25%   1 hour.

1-5 Degree exam   75%   2 hours.

The general aims of this course are to:

■ provide an overall introduction to the type of mathematics used extensively in finance;

■ provide a necessary foundation for further study of modern finance in the second semester courses.

By the end of the course students should be able to:

1. demonstrate skills based on data interpretation and numeracy;

2. deploy techniques of mathematical finance within a problem solving context;

3. analyse stochastic processes closely related to finance and apply stochastic calculus;

4. demonstrate an ability to construct a focused argument based on coherent general principles

5. discuss how well various stochastic processes function as models in finance and explain the limitations of these models;

Students must submit at least 75% by weight of the components (including examinations) of the course's summative assessment.