MVE565 / MMA630 Computational methods for stochastic differential equations

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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
15/1 ([G] Chp. 1-3) Introduction

Slides Lecture 1
18/1 [G] 4.1 - 4.2 Brownian motion, Itô integral Questions Lecture 2
22/1 [G] 4.2 - 4.3 remaining stochastic integral, stochastic differential equations Questions Lecture 3
25/1 [G] 4.4 - 4.5, 5.1

Feynman-Kac formulas
Euler-Maruyama scheme

 Questions Lecture 4
29/1

[G] 5.1 - 5.2

2 (new to you)

Euler-Maruyama scheme, strong convergence

Monte-Carlo methods

 Questions Lecture 5
1/2

[G] 5.3(-5.4), 6.1

Weak convergence

statistical errors

 Questions Lecture 6
5/2 [G] 6.2-6.3

 (Multilevel) Monte Carlo

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

[HRSW] 3.1 - 3.3

Sobolev spaces, variational formulation, Gelfand triplet, discretization

 Questions Lecture 9
15/2 [HRSW] 3.4-3.6

Implementation, stability and error analysis

 Questions Lecture 10
20/2
OBS switched with exercise class		 Discussion Project 1
22/2 [HRSW] 4.1-4.4
 BS SDE and PDE, variational formulation, localization, discretization Questions Lecture 11
26/2 [HRSW] 4.5, 8, 9 Extensions of BS to other models and higher dimensions (brief) Questions Lecture 12

4/3

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

 

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Recommended exercises

Preliminary list of exercises that might be adapted.

Exercise dates and content
Day Exercises
16/1 self preparation for lecture
23/1

4.1-4.2

E41 E42
30/1

4.3-4.4

E43 E44

 
6/2

Questions for Project 1
13/2

4.5, 5.1

E45 E51

19/2
OBS: switched with lecture

5.2-5.3

E52 E53
27/2

6.1-6.2

E61 E62

 

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 12, 2024, 07:00
Project 2: deadline March 7, 2024, 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:

Date Details Due