Course syllabus for Computational methods for stochastic differential equations

The course syllabus contains changes
See changes

Course syllabus adopted 2021-02-12 by Head of Programme (or corresponding).

Overview

  • Swedish nameBeräkningsmetoder för stokastiska differentialekvationer
  • CodeMVE565
  • Credits7.5 Credits
  • OwnerMPENM
  • Education cycleSecond-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 20135
  • Open for exchange studentsYes

Credit distribution

0119 Examination 7.5 c
Grading: TH		 7.5 c
  • 17 Mar 2022 pm J
  • 10 Jun 2022 am J
  • Contact examiner

In programmes

Examiner

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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.

Aim

Students will learn how to efficiently compute solutions and so-called Quantities of Interest to stochastic differential equations. Different approximation strategies are introduced and their quality is judged with strong and weak convergence analysis. The interaction of mathematical theory and practical implementations plays a crucial role in the understanding of the course content.

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).

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.

The course syllabus contains changes

  • Changes to examination:
    • 2022-04-23: Exam date Exam date changed by Elisabeth Eriksson
      [34749, 55300, 3], New exam for academic_year 2021/2022, ordinal 3 (not discontinued course)
    • 2022-04-13: Cancelled Changed to cancelled by Examinator/Adm
      [2022-06-10 7,5 hec, 0119] Cancelled
    • 2022-01-17: Exam date Exam date changed by Elisabeth Eriksson
      [34749, 55300, 2], New exam for academic_year 2021/2022, ordinal 2 (not discontinued course)