Professor Mihail Zervos, COL 4.02 and Dr Tugkan Batu, COL 4.04

This course is primarily intended for students studying on MSc Financial Mathematics and MSc Risk and Stochastics. Students on these programmes are required to attend the pre-sessional course prior to starting their degree programme.

The course is also available to other suitably qualified students with the permission of the Degree Programme Director and the teacher responsible for the course.

The purpose of this course is to review some key concepts of finance and probability and to discuss a range of mathematical definitions and techniques that set the agenda for the Financial Mathematics MSc as a whole. Also, this course will incorporate an introduction to programming with C++.

This course is composed of two components:

The first component is concerned with 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: a review of sets and set operations, functions and inverse functions is first developed; probability spaces, random variables, distributions, expectations and moment generating functions are then discussed; special emphasis is placed on the binomial, the normal and the log-normal distributions; 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 and the Poisson process are introduced; Itô's formula and Girsanov's theorem are discussed on a formal basis.

The second component is an introduction to programming with languages such as C++.

40 lectures and classes over two weeks during September, prior to the start of the academic year, and 3 support lectures in MT.

Exercises are assigned and form the basis of class discussion.

Lecture notes will be provided for the mathematics component of this module. For the programming elements of the pre-sessional, we will use Derek Capper, Introducing C++ for Scientists, Engineers and Mathematicians, Springer 2001. For those with prior programming experience, a standard reference book on the C++ programming language is Bjarne Stroustrup, The C++ Programming Language, Addison Wesley, 1997.

This course does not form part of the degree award.