MVE565 / MMA630 Computational methods for stochastic differential equations Spring 26

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This page contains the program of the course: lectures, exercise sessions and projects. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.

Program

The schedule of the course is in TimeEdit Links to an external site..

Lectures

Below you find the preliminary schedule based on the last iteration of the course. We will adapt the speed to the group and interest of the participants.

Lecture dates and content
Day Sections Content Questions

Slides & notes
19/1 ([G] Chp. 1-3) Introduction

Slides Lecture 1 Download Slides Lecture 1
22/1 [G] 4.1 - 4.2 Brownian motion, Itô integral

Lecture 2 Download Lecture 2
(as in slides above)
26/1 [G] 4.2 - 4.3 remaining stochastic integral, stochastic differential equations Lecture 3 Download Lecture 3 (see also Lecture 2)
29/1 [G] 4.4 - (4.5), 5.1

Feynman-Kac formulas
Euler-Maruyama scheme

 Lecture 4 Download Lecture 4
2/2

[G] 5.1 - 5.2

2 (new to you)

Euler-Maruyama scheme, strong convergence

Monte-Carlo methods

 Lecture 5 Download Lecture 5
5/2

[G] 5.3(-5.4), 6.1

Weak convergence

statistical errors

 Lecture 6 Download Lecture 6
9/2 [G] 6.2-6.3

 (Multilevel) Monte Carlo

 Lecture 7 Download Lecture 7
12/2 [G] 4-6 Repetition [G] Lecture 8 Download Lecture 8
16/2

[HRSW] 3.1

Sobolev spaces,  Gelfand triplet

 Lecture 9 Download Lecture 9
19/2

[HRSW] 3.2 - 3.4

Variational formulation, Gelfand triplet, discretization, implementation

 see Lecture 9 Download Lecture 9
23/2 [HRSW] 3.4-3.6

Implementation, stability and error analysis

 Lecture 10 Download Lecture 10
26/2 [HRSW] 3.6.2, 4.1-4.4
 FE error, BS SDE and PDE, variational formulation, localization, discretization see above & Lecture 11
2/3 Discussion Project 1

5/3

 [HRSW] 4.5, 8, 9 Extensions of BS to other models and higher dimensions

9/3

 [HRSW] Repetition [HRSW] and all remaining questions for both parts of the course

12/3

 Discussion Project 2

 

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Recommended exercises

Preliminary list of exercises that might be adapted.

Exercise dates and content
Day Exercises
20/1

Introduction to exercises.
Euler ODE notes.pdf Download Euler ODE notes.pdf 
27/1

4.1-4.2 ES1.pdf Download ES1.pdf
3/2

4.3-4.4 ES2.pdf Download ES2.pdf
10/2

Questions for Project 1
17/2

ES3.pdf Download ES3.pdf

24/2

ES4.pdf Download ES4.pdf
3/3

Questions for Project 2
10/3

 

Exercises and hints for exercise sessions: Here

 

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Projects

Two projects can be handed in for up to four bonus points per project on the ordinary exam. Reports are written and submitted individually.
Project 1 Download Project 1: deadline February 23, 2026, 07:00
Project 2 Download Project 2: deadline March 9, 2026, 07:00

Reference literature:

  1. [G] Emmanuel Gobet: Monte-Carlo Methods and Stochastic Processes: From Linear to Non-Linear Links to an external site., CRC, 2016

  2. [HRSW] Norbert Hilber, Oleg Reichmann, Christoph Schwab, Christoph Winter: Computational Methods for Quantitative Finance: Finite Element Methods for Derivative Pricing Links to an external site., Springer, 2013
  3. [KP] Peter Kloeden, Eckhard Platen: Numerical Solutions of Stochastic Differential Equations Links to an external site., Springer, 1992
  4. [Ø] Bernt Øksendal: Stochastic Differential Equations: An Introduction with Applications Links to an external site., Springer, 2003
  5. Learning MATLAB, Tobin A. Driscoll. Provides a brief introduction to Matlab to the one who already knows computer programming. Available as e-book from Chalmers library Links to an external site..
  6. Physical Modeling in MATLAB 3/E, Allen B. Downey
    The book is free to download from the web Links to an external site.. The book gives an introduction for those who have not programmed before. It covers basic MATLAB programming with a focus on modeling and simulation of physical systems.

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Course summary:

Course Summary
Date Details Due