Dr Albina Danilova

This course is compulsory on the MSc in Financial Mathematics and MSc in Quantitative Methods for Risk Management. This course is available with permission as an outside option to students on other programmes where regulations permit.

Students who wish to select this course as an outside option must have a quantitative background.

The purpose of this course is to review some key concepts of probability used in finance. The course develops the common mathematical background that is assumed by the MSc Financial Mathematics and addresses some aspects of the mathematical theory that is central to the foundations of the programme: probability spaces, random variables, distributions, expectations and moment generating functions are reviewed; the concepts of conditional probability and conditional expectation as random variables are introduced using intuitive arguments and simple examples; stochastic processes, martingales, the standard Brownian motion are introduced; Itô integrals, Itô's formula and Girsanov's theorem are discussed on a formal basis.

This course is delivered through a combination of classes and lectures over two weeks in September, prior to the start of the academic year. The material covered in the lectures will be totalling to an amount of roughly 30 hours of lecturing and 8 hours of seminars. The teaching will generally be in person, but some of the material maybe delivered via online videos or video link. There will be an informal examination at the end of the course.  Its purpose is to provide student feedback and it does not count towards the degree.

Exercises are assigned and form the basis of class discussion.

Lecture notes will be provided.

S. Shreve, Stochastic Calculus for Finance II Continuous-Time Models, Springer.

D. Williams, Probability with Martingales, Cambridge University Press.

This course does not form part of the degree award.