MF002 Stochastical analysis

Faculty of Science
Spring 2009
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)
doc. RNDr. Petr Lánský, DrSc. (lecturer)
Mgr. Ondřej Pokora, Ph.D. (seminar tutor)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 14:00–15:50 01031
  • Timetable of Seminar Groups:
MF002/01: Wed 16:00–16:50 01031
Prerequisites
Calculus in one and several variables
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
The main objective of the course is to learn basic techniques of the Ito stochastic integral calculus and its applications in economics and finance. At the end of the course, students shuld be able to understand and use stochastic calculus in economic and financial modelling.
Syllabus
  • Brownian motion with drift
  • Linear and quadratic variation
  • Stochastic integral
  • Ito lemma
  • Martigale representation theorem
  • Likelihood ratio
  • Cameron-Martin theorem
  • Girsanov theorem
  • Stochastic interpretation of difusion and Lalace equation
  • Feynman-Kac theorem
  • Stratonovic integral
Literature
  • KARATZAS, Ioannis and Steven E. SHREVE. Methods of mathematical finance. New York: Springer-Verlag, 1998, xv, 415. ISBN 0387948392. info
  • KARATZAS, Ioannis and Steven E. SHREVE. Brownian motion and stochastic calculus. New York: Springer, 1988, 23, 470. ISBN 0387976558. info
Assessment methods
Oral exam
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 Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.
  • Enrolment Statistics (Spring 2009, recent)
  • Permalink: https://is.muni.cz/course/sci/spring2009/MF002