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

Day Sections Content Questions

Slides & notes
20/1 ([G] Chp. 1-3) Introduction

Lecture 1

Lecture 1 annotated
23/1 [G] 4.1 - 4.2 Brownian motion, Itô integral Questions Lecture 2
27/1 [G] 4.2 - 4.3 Itô integral, stochastic differential equations Questions Lecture 3
28/1 [G] 4.3, 4.4 - 4.5

cont. SDE

Feynman-Kac formulas

 Questions Lecture 4
3/2 [G] 4.4-4.5, 5.1 - 5.2

cont. Feynman-Kac

Euler-Maruyama scheme, strong convergence

 Questions Lecture 5
6/2

[G] 5.1 - 5.2

2 (new for you)

Monte Carlo methods

strong convergence

 Questions Lecture 6
10/2 [G] 5.3(-5.4), 6.1

Weak convergence

statistical errors

 Questions Lecture 7
11/2 [G] 6.1-6.3 (Multilevel) Monte Carlo Questions Lecture 8
17/2

[G] 6

 

Discussion Project 1

Repetition [G]

(Multilevel Monte Carlo)
20/2 [HRSW] 3.1

Cont. discussion Project 1 and repetition [G]

Sobolev spaces
24/2 [HRSW] 3.1-3.2 Sobolev spaces and variational formulation, Gelfand triplet Questions Lecture 11
27/2 [HRSW] 3.2-3.4 Variational formulation, discretization and matrix form Questions Lecture 12
2/3 [HRSW] 3.5-3.6 Stability and error analysis Questions Lecture 13
5/3 [HRSW] 4.3 Localization (based on the given section)

 

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Recommended exercises

Hints on certain exercises: pdf

Day Exercises
30/1 4.1-4.2
4/2 4.3-4.4
13/2 4.5,5.1
18/2 5.2-5.3
25/2 6.1-6.2
3/3

 

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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 17, 2020, 07:00
Project 2: deadline March 12, 2020, 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