Measure Theory and Stochastic Processes II
2012-2013
Duisenberg School of Finance

Aim

To make students familiar with the mathematical fundamentals of stochastic processes and stochastic integrals.

Contents

Construction of Brownian motion from symmetric walk by the central limit theorem, martingale property and quadratic variation; construction of the Itô integral, fundamental properties (Itô isometry); Itô rule (in one and more dimensions), stochastic product rule, Lévy's characterization of Brownian motion; absolutely continuous change of measure, Girsanov's theorem, martingale representation theorem; stochastic differential equations, diffusions and partial differential equations, Feynman-Kaç formula, stopping times; Poisson and compound Poisson process, decomposition of compound Poisson processes, quadratic variation, Itô formula for processes with jumps, change of measure for jump-diffusions, extension of Girsanov's theorem.

Prerequisites

Basic concepts of probability and measure theory, as given in the course on Measure and Probability by Laurens de Haan.

Literature

The course is mainly based on Steve Shreve, Stochastic Calculus for Finance II, Continuous-Time Models, Springer (2004).

Examination

Weekly a set of homework assignments and a final written exam at the end. You are required to work in pairs (and a pair means two people only!) for the homework. Deadlines are always a week after the assignment has been made known. The written exam is on Wednesday 9 January 2013, 10.00-13.00.

People

Lectures by Peter Spreij, tutorials by Marius Zoican. See also the extra TA information webpage by Marius.

Schedule