Dr George Tzougas COL.7.04

This course is compulsory on the MSc in Quantitative Methods for Risk Management. This course is available on the MSc in Accounting and Finance, MSc in Finance (full-time), MSc in Financial Mathematics, MSc in Statistics (Financial Statistics) and MSc in Statistics (Financial 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).

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.

20 hours of lectures and 10 hours of workshops in the LT.

Week 6 will be used as a reading week.

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.

Exam (50%, duration: 2 hours) in the main exam period.
Project (50%) in the ST.