Dr Erik Baurdoux COL 6.04

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

This course builds on material discussed in ST409 (Stochastic Processes). In particular, elements of the general theory of semi-martingales will be covered and emphasis will be given on presenting a variety of models involving processes with general dynamics, including jumps. The theory will be applied to a range of topics in mathematical finance and insurance, as well as financial economics.

20 hours of lectures and 10 hours of seminars in the WT. 2 hours of lectures in the ST.

Week 6 will be used as a reading week; exercises will be given out to students to do at home.

A set of coursework similar to the exercises that will appear in the exam will be assigned. Additional formative exercise will be available through Moodle.

Brownian Motion and Stochastic Calculus. Ioannis Karatzas and Steve Shreve

Numerical Solution of Stochastic Differential Equations with Jumps in Finance. Eckhard Platten, Nicola Bruti-Liberati.

Essentials of Stochastic Finance: Facts, Models, Theory. Albert Shiryaev.

Stochastic Integration and Differential Equations. Phillip Protter.

Levy Processes in Finance: Pricing Financial Derivatives. Wim Schoutens

Fluctuations of Lévy Processes with Applications. Andreas Kyprianou

Selected papers from scientific journals.

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