TKK / Institute of Mathematics / teaching /
The purpose is to give introduction to discrete time martingale theory and stochastic calculus with respect to continuous martingales, in particular with respect to standard Brownian motion.
Prerequisites (recommended):
Mat-1.3601 Johdatus stokastiikkaan/Introduction to Stochastics
Mat-2.3111 Stokastiset prosessit/Stochastic Processes
Contents:
1. Conditional expectation
2. Discrete time martingales
3. Brownian motion and continuous martingales
4. Stochastic integrals
5. Applications, part I: Girsanov theorem, Levy theorem, iterated
integrals
6. Stochastic differential equations
7. Applications, part II [if the time permits]
Lectures:
Professor Esko
Valkeila
Th 9 - 12 U261 Tu 9 - 12 Y405
First lecture Th 13.03. 2008 and last lecture Tu 29.04. 2008
Language: Finnish [English on demand]
Exams: May 16, 13 - 16
Exercises:
Assistant
Ehsan
Azmoodeh
Language: English
Exercise class Th 14-16 U356
Exeptionally first exercise class Tu 18.03. 2008, 14-16 U356 and last exercise class Tu 29.04. 14-16 U356
Course material:
Typeset handouts based on the following references: