MF002 Stochastical analysis

Faculty of Science
Spring 2012
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
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Fri 11:00–12:50 M3,01023, Fri 12:00–13:50 MP2,01014a
  • Timetable of Seminar Groups:
MF002/01: Fri 13:00–13:50 M3,01023, M. Kolář
Prerequisites
Calculus in one and several variables
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
At the end of the course students should be able to: define the Ito and Stratonovich stochastic integrals; solve basic types of stochastic differential equations; prove the Ito Lemma and further properties of stochastic integral; apply stochastic calculus to problems in financial mathematics
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 diffusion and Laplace equation
  • Feynman-Kac theorem
  • Stratonovich integral
Literature
  • MELICHERČÍK, Igor, Ladislava OLŠAROVÁ and Vladimír ÚRADNÍČEK. Kapitoly z finančnej matematiky. [Bratislava: Miroslav Mračko, 2005, 242 s. ISBN 8080576513. info
  • ØKSENDAL, Bernt. Stochastic differential equations : an introduction with applications. 6th ed. Berlin: Springer, 2005, xxvii, 365. ISBN 3540047581. info
  • HULL, John. Options, futures & other derivatives. 5th ed. Upper Saddle River: Prentice Hall, 2003, xxi, 744. ISBN 0130090565. info
  • 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
Teaching methods
Lectures, class discussions, homeworks, excercises
Assessment methods
Oral exam
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 Spring 2008 - for the purpose of the accreditation, Spring 2011 - only for the accreditation, Spring 2009, Spring 2010, Spring 2011, 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 2012, recent)
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