#
PřF:MF001 Stochastical processes in fina - Course Information

## MF001 Stochastical processes in financial mathematics

**Faculty 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).
**Teacher(s)**- doc. RNDr. Martin Kolář, Ph.D. (lecturer)
**Guaranteed by**- prof. RNDr. Ivanka Horová, CSc.

Department of Mathematics and Statistics - Departments - Faculty of Science **Prerequisites**- 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.
**Syllabus**- Random walk
- The reflection principle
- Markov property
- Polya's theorem
- arcsine laws
- discrete martingales
- filtrations
- martingale transform
- Wiener process
- Cieselski's construction of brownian motion
- Continuous time martingales and filtrations

**Literature**- 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**- Czech
**Further Comments**- The course is taught annually.

The course is taught: every week. **Listed among pre-requisites of other courses**

- Enrolment Statistics (Autumn 2010 - only for the accreditation, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2010-onlyfortheaccreditation/MF001