Course title:

Professor(s):

Prof. Freddy Delbaen
Prof. Thorsten Rheinländer
Prof. Uwe Schmock
Prof. Philipp J. Schönbucher

Total hours of lectures and seminars:

14 x 2 = 28 hours

Date and Time:

Starting from 22^nd of October 2002

Tuesdays 15:00 – 17:00

City:

Zurich

Room:

ETHZ, HG E1.2

Contents of the course:

• Review of probabilistic notation (probability spaces; random variables, product spaces; filtrations; trees; atoms; transition probabilities
• Definition of adapted and predictable stochastic processes
• Conditional expectations (definition and basic properties)
• Martingales, submartingales, supermartingales (definition and basic properties)
• Stopping times and their sigma-algebras
• Bayes' formula in connection with conditional expectations
• Weak convergence
• Central limit theorem
• Snell envelopes
• Decomposition of supermartingales
• Brownian motion and its properties
• Brownian motion with drift
• Introduction to stochastic integration
• Itô's lemma, Girsanov-Maruyama theorem
• Stochastic differential equations