PřF:MF001 Stochastical processes in fina - Course Information
MF001 Stochastical processes in financial mathematicsFaculty of Science
Autumn 2010 - only for the accreditation
- Extent and Intensity
- 2/1. 3 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
- doc. RNDr. Martin Kolář, Ph.D. (lecturer)
- Guaranteed by
- prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics - Departments - Faculty of Science
- Calculus, probability theory
- Course Enrolment Limitations
- The course is also offered to the students of the fields other than those the course is directly associated with.
- fields of study / plans the course is directly associated with
- Finance Mathematics (programme PřF, N-AM)
- Course objectives
- At the end of the course students should be able to: define random walk, the Wiener process and other basic concepts; solve problems concerning trajectories and recurence of random walk; prove Polya's theorem on returns to the origin and other basic results; apply the processes in mathematical modelling in finance.
- Random walk
- The reflection principle
- Markov property
- Polya's theorem
- arcsine laws
- discrete martingales
- martingale transform
- Wiener process
- Cieselski's construction of brownian motion
- Continuous time martingales and filtrations
- J. Michael Steele, Stochastic Calculus and Financial Applications, ISBN 0387950168, Springer-Verlag, 2003
- GRIMMETT, Geoffrey R. and David STIRZAKER. Probability and random processes. 3rd ed. Oxford: Oxford University Press, 2001. xii, 596 s. ISBN 0-19-857222-0. info
- Teaching methods
- Lectures, class exercises and homeworks
- Assessment methods
- oral exam
- Language of instruction
- Further Comments
- The course is taught annually.
The course is taught: every week.
- Listed among pre-requisites of other courses