MF001 Stochastical processes in financial mathematics

Faculty of Science
autumn 2021
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 8:00–9:50 M3,01023
  • Timetable of Seminar Groups:
MF001/01: Tue 10:00–10:50 M3,01023, 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
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
Oral examination.
Language of instruction
Czech
Further Comments
Study Materials
The course is taught annually.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (autumn 2021, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2021/MF001