Deutsch Intern
  • Lettering Team
Applied Stochastics

Stochastic processes

0803300 · Stochastic processes

Lecturer: Prof. Dr. Markus Bibinger

Tutor: Michael Sonntag

  • Date and location:  The course will be online. There are asynchronous lecture videos provided via WueCampus. There is also a synchronous part of the lecture via zoom on Tueday, 10:15-11:15 am.
  • Start: April 13, 2021
  • Exercises (Vst.-Nr.  0803305): Monday 4:15-5:45 pm / Note: the tutorial will be online via zoom.
  • Exams: Oral exams,  appointments are assigned later.
  • Registration for the exam: Via WueStudy, registration period will be announced on WueCampus.

Contents of the lecture:

This lecture is devoted to the theory of continuous-time stochastic processes. A first main topic is the construction of  the Wiener process and studying its properties. We discuss central classes of stochastic processes as Gaussian processes including fractional Brownian motion, Lévy processes and semi-martingales. A main goal of the lecture is to develop the theory of stochastic integration and Itô calculus. As an application, we derive the most important results of mathematical finance.

In particular, the lecture contains the following contents:

  • Conditional expectation and martingal theory
  • Brownian motion
  • Filtrations and continuous-time martingales
  • Gaussian processes and fractional Brownian motion
  • Regularity of stochastic processes
  • Itô integration and semi-martingales
  • Stochastic differential equations
  • Markov processes
  • Financial mathematics (Black-Scholes formula, fundamental theorem of asset pricing)

Literature:

  • Karatzas, I. and S. E. Shreve: Brownian motion and stochastic calculus. Springer-Verlag, New York, 1991.
  • Klenke, A.: Wahrscheinlichkeitstheorie, Springer, 2008.
  • Protter, P. E.: Stochastic integration and differential equations. Springer-Verlag, Berlin, 2003.
  • Shreve, S. E.: Stochastic calculus for finance II. Continuous-time models. Springer Finance. New York, 2004.
  • Revuz, D. and M. Yor: Continuous martingales and Brownian motion. Springer-Verlag, Berlin, 1999.

 

Notes:

(1) Registration (Vst.-Nr. 0803305) in WueStudy is required!

(2) Materials (lecture notes, videos, exercise sheets) via WueCampus (Link ).