Dr Arne Lokka, COL 4.08

This course is primarily intended for students studying for MSc Financial Mathematics, MSc Applicable Mathematics, MSc Accounting and Finance and MSc Management and Regulation of Risk.

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

MA411 Probability and Measure, or ST409 Stochastic Processes, or equivalent.

This course is concerned with a rigorous introduction to the area of stochastic analysis with emphasis on Itô calculus.

The course begins necessary preliminaries, followed by a construction of the standard Browian motion and a study of its properties. Subsequently, Lévy's characterisation of Browian motion, martingale representation theorems and Girsanov's theorem are established. The course then expands on a study of stochastic differential equations.

20 lectures and 10 seminars in the Lent Term.

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

Full lecture notes will be provided.

The following may prove useful:

I Karatzas and S E Shreve, Brownian Motion and Stochastic Calculus, Springer; B Øksendal, Stochastic Differential Equations: An Introduction with Applications, Springer; D Revuz and M Yor, Continuous Martingales and Brownian Motion, Springer; L C G Rogers and D Williams, Diffusions, Markov Processes, and Martingales, Cambridge.

A two-hour exam in the Summer Term.