Dr Arne Lokka

This course is available on the MSc in Applicable Mathematics and MSc in Financial Mathematics. This course is available with permission as an outside option to students on other programmes where regulations permit.

ST409 or MA411.

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 Brownian motion and a study of its properties. Subsequently, Lévy’s characterisation of Brownian motion, martingale representation theorems and Girsanov’s theorem are established. The course then expands on a study of stochastic differential equations.

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

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.

Exam (100%, duration: 2 hours) in the summer exam period.