#
PřF:MF001 Stochastical processes in fina - Course Information

## MF001 Stochastical processes in financial mathematics

**Faculty of Science**

Autumn 2019

**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**- doc. RNDr. Martin Kolář, Ph.D.

Department of Mathematics and Statistics - Departments - Faculty of Science

Supplier department: Department of Mathematics and Statistics - Departments - Faculty of Science **Timetable**- Tue 16:00–17:50 M6,01011
- Timetable of Seminar Groups:

*M. Kolář* **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-MA)

**Course objectives**- This is an introductory course in stochastic processes and their applications in Financial mathematics. It covers in detail Random walk and further discrete models for pricing financial derivatives. The end of the course is devoted to the passage to the continuous case, namely the Wiener process and Black-Scholes model.
**Learning outcomes**- 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
- Poisson process
- Cramér-Lundberg model
- discrete martingales
- filtrations
- martingale transform
- Wiener process
- Derivation of the Black-Scholes equation

**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 homework
**Assessment methods**- Two written tests during the semester, consisting of 5 problems each. 50% of total points is needed to pass. Oral examination.
**Language of instruction**- Czech
**Further Comments**- Study Materials

The course is taught annually. **Listed among pre-requisites of other courses**

- Enrolment Statistics (Autumn 2019, recent)
- Permalink: https://is.muni.cz/course/sci/autumn2019/MF001