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Syllabus for

Academic year
MVE565 - Computational methods for stochastic differential equations  
Beräkningsmetoder för stokastiska differentialekvationer
 
Syllabus adopted 2020-03-12 by Head of Programme (or corresponding)
Owner: MPENM
7,5 Credits
Grading: TH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail
Education cycle: Second-cycle
Major subject: Mathematics
Department: 11 - MATHEMATICAL SCIENCES

The course round is cancelled. For further questions, please contact the director of studies MPENM: ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, contact information can be found here


Teaching language: English
Application code: 20115
Open for exchange students: Yes

Module   Credit distribution   Examination dates
Sp1 Sp2 Sp3 Sp4 Summer course No Sp
0119 Examination 7,5c Grading: TH   7,5c    

In programs

MPENM ENGINEERING MATHEMATICS AND COMPUTATIONAL SCIENCE, MSC PROGR, Year 1 (compulsory elective)

Examiner:

Annika Lang

  Go to Course Homepage


Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

General entry requirements and the equivalent of the courses TMS165 Stochastic Calculus and TMA372 Partial Differential Equations.

Learning outcomes (after completion of the course the student should be able to)

On successful completion of the course the student will be able to:
  • compute quantities of interest of solutions to stochastic differential equations (SDEs) with SDE approximation schemes and Monte Carlo methods,
  • derive partial differential equations corresponding to the quantities of interest,
  • compute solutions to the derived partial differential equations with finite element methods,
  • analyze the errors of the used approximations.

Content

Euler-Maruyama and Milstein approximations of solutions to stochastic differential equations. Strong and weak convergence analysis. Monte Carlo and multilevel Monte Carlo methods. Kolmogorov backward equations. Approximation of solutions to these partial differential equations with finite element methods. Error analysis. Computational complexity. Applications in finance and engineering.

Organisation

Lectures and exercise classes.

Literature

The course literature is given on a separate list.

Examination including compulsory elements

There will be a written examination at the end of the course. During the course, there may be optional assignments that give bonus points on the exam. Examples of such assignments are small written tests, labs, and oral or written presentations. Information about this is found on the course home page.
If a student, who has failed the same examined component twice, wishes to change examiner before the next examination, a written application shall be sent to the department responsible for the course and shall be granted unless there are special reasons to the contrary (Chapter 6, Section 22 of Higher Education Ordinance).


Published: Mon 28 Nov 2016.