MMA630, Computational methods for stochastic differential equations, Spring 19

Latest news

Welcome to the course! The schedule for the course can be found in TimeEdit.

There are no assigned course representatives for the course this year but we discuss the evaluation with all participants due to the small number. This was decided in the lecture.

25/1: Do not forget to read and understand the chapters in the book before the lecture.
5/2: Added project deadline. Note that the discussion after the final presentation also may include an examination of the lecture content. This is necessary if you did not actively participate in the lectures and discussions (which we agreed on in the first lecture).
5/2: In case that you are NOT attending the lectures, be aware that this is no MOOC course and that the homepage is not compensating an active lecture participation.

Teachers

Course coordinator: Annika Lang

Teaching assistants: Per Ljung

Course literature

Main literature:

[G] Emmanuel Gobet: Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear, CRC, 2016
[HRSW] Norbert Hilber, Oleg Reichmann, Christoph Schwab, Christoph Winter: Computational Methods for Quantitative Finance: Finite Element Methods for Derivative Pricing, Springer, 2013
[KP] Peter Kloeden, Eckhard Platen: Numerical Solutions of Stochastic Differential Equations, Springer, 1992
[Ø] Bernt Øksendal: Stochastic Differential Equations: An Introduction with Applications, Springer, 2003

English-Swedish mathematical dictionary

Program

Lectures

Day	Sections	Contents
24/1 - 1		Introduction
24/1 - 2	([G] Chp. 1-3)	Introduction to random number generation
28/1	[G] 4.1 - 4.3	Brownian motion, Itö integral, stochastic differential equations
31/1	[G] 4.2 - 4.3	Itô integral, SDEs
4/2	[G] 4.4 - 4.5	Feynman-Kac formulas
7/2	[G] 5.1 - 5.2	Euler-Maruyama scheme, strong convergence
11/2	[G] 5.3, (5.4)	Weak convergence
14/2	[G] 6.1 - 6.2	Statistical errors, Monte Carlo method
18/2	[G] 6.3 - 6.5	Multilevel Monte Carlo
21/2	[HRSW] 3	Review on FEM for parabolic PDEs
25/2	[HRSW] 4	PDE in 1-d
28/2	[HRSW] 8	Multidimensional PDEs
4/3	[HRSW] 9, notes	CIR process, Heston model
5/3		Project discussions and feedback
22/3		Project presentations

Recommended exercises

Day	Exercises
29/1	Ex. 4.1 - 4.2
5/2	Ex. 4.3 - 4.4
12/2	Ex. 4.5, 5.1
19/2	Ex. 5.2, 5.3
26/2	Ex. 6.1, 6.2
7/3	Projects

Computer labs

Reference literature:

Learning MATLAB, Tobin A. Driscoll ISBN: 978-0-898716-83-2 (The book is published by SIAM).

Course requirements

The learning goals of the course can be found in the course plan.

Project

Submission of the project report: 14/3 - 2019

Project presentation: 22/3 - 2019, 9.00 - 12.00, MVF32

The project report (length of the main part around 10-15 pages, else contact the examiner) is written in latex. It is submitted as one pdf file no later than the deadline by sending an email to annika.lang@chalmers.se and annika.lang.chalmers@analys.urkund.se. The reports are then distributed to all participants of the course which read the reports before the presentation. All students are required to participate in all presentations of the projects and take part in an active discussion after the presentation. Presentation and discussion should not exceed 20 minutes in total (e.g., 15 + 5) and are not limited to the content of the project but to all lecture content.

Examination

The examination 2019 consists of a written project report and a presentation of the report with discussion. For details on the project, see "Project" above.

Examination procedures

In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers. In addition to that, there is a schedule when exams are given for courses at University of Gothenburg.

Before the exam, it is important that you sign up for the examination. If you study at Chalmers, you will do this by the Chalmers Student Portal, and if you study at University of Gothenburg, you sign up via GU's Student Portal, where you also can read about what rules apply to examination at University of Gothenburg.

At the exam, you should be able to show valid identification.

After the exam has been graded, you can see your results in Ladok by logging on to your Student portal.

At the annual (regular) examination:
When it is practical, a separate review is arranged. The date of the review will be announced here on the course homepage. Anyone who can not participate in the review may thereafter retrieve and review their exam at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

At re-examination:
Exams are reviewed and retrieved at the Mathematical Sciences Student office. Check that you have the right grades and score. Any complaints about the marking must be submitted in writing at the office, where there is a form to fill out.

Old exams

This is the first time the course is given, therefore no old exams exist.