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
26/1 [G] 4.2 - 4.3 remaining stochastic integral, stochastic differential equations
29/1 [G] 4.4 - 4.5, 5.1

Feynman-Kac formulas
Euler-Maruyama scheme
2/2

[G] 5.1 - 5.2

2 (new to you)

Euler-Maruyama scheme, strong convergence

Monte-Carlo methods
5/2

[G] 5.3(-5.4), 6.1

Weak convergence

statistical errors
9/2 [G] 6.2-6.3

 (Multilevel) Monte Carlo
12/2 [G] 4-6 Repetition [G]
16/2

[HRSW] 3.1 - 3.3

Sobolev spaces, variational formulation, Gelfand triplet, discretization
19/2 [HRSW] 3.4-3.6

Implementation, stability and error analysis
23/2 Discussion Project 1
26/2 [HRSW] 4.1-4.4
 BS SDE and PDE, variational formulation, localization, discretization
2/3 [HRSW] 4.5, 8, 9 Extensions of BS to other models and higher dimensions (brief)

5/3

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

9/3

 TBA

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

 
10/2

Questions for Project 1
17/2

 

24/2

 
3/3

 
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: deadline February 16, 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