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.

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

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

Feynman-Kac formulas
Euler-Maruyama scheme

 Lecture 4
2/2

[G] 5.1 - 5.2

2 (new to you)

Euler-Maruyama scheme, strong convergence

Monte-Carlo methods

 Lecture 5
5/2

[G] 5.3(-5.4), 6.1

Weak convergence

statistical errors

 Lecture 6
9/2 [G] 6.2-6.3

 (Multilevel) Monte Carlo

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

[HRSW] 3.1

Sobolev spaces,  Gelfand triplet

 Lecture 9
19/2

[HRSW] 3.2 - 3.4

Variational formulation, Gelfand triplet, discretization, implementation

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

Implementation, stability and error analysis

 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 Lecture 12

9/3

 [HRSW] Repetition [HRSW] and all remaining questions for both parts of the course Lecture 13

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
27/1

ES1.pdf
3/2

ES2.pdf
10/2

Questions for Project 1
17/2

ES3.pdf

24/2

ES4.pdf
3/3

Questions for Project 2
10/3

ES5.pdf

Solutions for exercises: exercise_solutions.pdf

 

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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: deadline February 23, 2026, 07:00
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, CRC, 2016

  2. [HRSW] Norbert Hilber, Oleg Reichmann, Christoph Schwab, Christoph Winter: Computational Methods for Quantitative Finance: Finite Element Methods for Derivative Pricing, Springer, 2013
  3. [KP] Peter Kloeden, Eckhard Platen: Numerical Solutions of Stochastic Differential Equations, Springer, 1992
  4. [Ø] Bernt Øksendal: Stochastic Differential Equations: An Introduction with Applications, 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.
  6. Physical Modeling in MATLAB 3/E, Allen B. Downey
    The book is free to download from the web. 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