MF001 Stochastical processes in financial mathematics

Faculty of Science
Autumn 2008
Extent and Intensity
2/1. 3 credit(s) (fasci plus compl plus > 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
Timetable
Mon 11:00–12:50 MS1,01016
  • Timetable of Seminar Groups:
MF001/01: Tue 10:00–10:50 MS1,01016, 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
The main aim of the course is to teach students fundamental methods of analysis of stochastic processes, used in mathematical modelling in finance, namely random walk and Wiener process. At the end of the course students will be able to use such processes in mathematical modelling, and master the techniques of their analysis.
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
Assessment methods
Teaching: lectures and class exercises. Exam: oral
Language of instruction
Czech
Further Comments
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 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 2021, Autumn 2022, Autumn 2023, Autumn 2024.
  • Enrolment Statistics (Autumn 2008, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2008/MF001