Dr Yufei Zhang

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

Students must have completed September Introductory Course (Financial Mathematics and Quantitative Methods for Risk Management) (MA400).

Any students who are taking ST433 as an optional course and who have not completed MA400 need to obtain permission from the lecturer by providing a statement explaining why and how they know the material covered in MA400.

The purpose of this course is to (a) develop the students' computational skills, (b) introduce a range of numerical techniques of importance in actuarial and financial engineering, and (c) develop the ability of the students to apply the theory from the taught courses to practical problems, work out solutions including numerical work, and to present the results in a written report.

Binomial and trinomial trees. Random number generation, the fundamentals of Monte Carlo simulation and a number of related issues. Finite difference schemes for the solution of ordinary and partial differential equations arising in insurance and finance. Numerical solutions to stochastic differential equations and their implementation. The course ends with an introduction to guidelines for writing a scholarly report/thesis.

This course will be delivered through a combination of classes, lectures and Q&A sessions totalling a minimum of 32 hours across Lent Term.

Weekly exercises and practicals are set and form the basis of the classes.

N E Steenrod, P Halmos, M M Schiffer & J A Dieudonne, How to write mathematics (1973); D.J. Duffy, Finite Difference Methods in Financial Engineering: A Partial Differential Equation Approach, Wiley; P. Glasserman, MonteCarlo Methods in Financial Engineering, Springer; P.E. Kloden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer. Further material will be specified during the course.

Project (100%) in the ST.