September Introductory Course (Financial Mathematics and Quantitative Methods for Risk Management)

This information is for the 2021/22 session.

Teacher responsible

Dr Christoph Czichowsky


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.

Course content

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.  This year, some or all of the teaching will be delivered through a combination of virtual classes and lectures delivered as online videos.  The material covered in the lectures will be totalling to an amount of roughly 30 hours of lecturing.  There will be 8 hours via 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.


Formative coursework

Exercises are assigned and form the basis of class discussion.

Indicative reading

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.

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.

Important information in response to COVID-19

Please note that during 2021/22 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the differing needs of students in attendance on campus and those who might be studying online. For example, this may involve changes to the mode of teaching delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

Key facts

Department: Mathematics

Total students 2020/21: 63

Average class size 2020/21: Unavailable

Controlled access 2020/21: No

Value: Non-credit bearing

Guidelines for interpreting course guide information

Personal development skills

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