Course information
News
The lecture that was originally scheduled on April 4 has been cancelled.
The choice of topics for the final projects will be discussed on the lecture April 18. See more below.
The project presentations will take place on Monday May 9 and the extra lecture on Tuesday May 10.
The schedule for the project presentations (i.e. which groups are to present each day) can be found below.
The list of questions to prepare for to the exam is now complete. All questions on the exam will be taken from the list.
The grading of the exam will be strict, see more below.
For information on the re-exam, see below.
General student information
Information on course registration, exam application etc. can be found on the Student affairs office website.
Teaching and assessment
The course is assessed is by a set of homework, a project, and a final written exam, all mandatory to pass the course. The homework and projects are carried out by groups of students. Each group hand in a report on each assignment. Graduate students, who wish to take the course SF3581, need to achieve a result corresponding to the grade C on SF2522, in order to pass SF3581.
Each homework and the project gives a maximum of 5 points, summing to a maximum of 30. The final written exam gives a maximum of 70 points. These points are added, and so the course grade is determined to 70% by the exam and 30% by the homeworks and project.
Homework
Each homework is presented orally (20 min) on the lecture the due date. The written report therefore needs to be handed in no later than at the "deadline" lecture.
Homework 1, due February 8. Note 1: For exercise 2 it is not necessary to use the definition of the stochastic integral as a limit of Forward Euler approximations (as is necessary in exercise 1). It is therefore allowed to use theorems in the literature, e.g. Theorem 2.16 in the lecture notes. Note 2: $x_0$ and $x_\infty$ are constants, not random variables.
Homework 2, due February 22.
Homework 3, due March 7.
Homework 4, due March 29.
Homework 5, due April 25.
Projects
Contact the lecturer regarding the topic for the project for you and your group. The problems will be presented by the groups according to a certain schedule during the lectures May 9 and 10. Prepare a 15 minutes presentation. Take the presentation seriously, and use it as an opportunity of getting some practical training in the difficult art of oral presentation. Remember that presenting a material in a clear and convincing way requires quite a bit of preparation and training to be successful. We all need practice and positive criticism in this respect, both teacher and students.
Schedule for project presentations
Monday May 9:
- Erik Berglund, Kristoffer Brodin, and Ludvig Hällman
- Aku Kammonen and Peyman Dabiri
- Jeroen Roseboom
- Najib Jamjam and Marouane Brahimi
- Alexios Kotsakis and Garrett Thomas
- Gustav Jonsson-Glans
Tuesday May 10
- Virginie Gauthier and Tarek Barbouche
- Erik Castillo and Sofia Karlsson
- Göran Svensson and Alexander Aurell
- Karl Jonsson
- Henrik Olsson, Alexander Söderstrand, and Lovisa Styrud
Preliminary course plan
| Lecture number | Content | Sections in lecture notes |
| 1 | Course introduction and overview. Basic probability theory | 1, 2.1 |
| 2 | Stochastic integrals | 2.2, 2.3 |
| 3 | Ito stochastic differential equations | 3.1 |
| 4 | Stratonovich SDE. Ito's formula. Systems of SDE | 3.2, 3.3, 3.4 |
| 5 | Kolmogorov forward and backward equations. Black-Scholes formula | 4.1, 4.2 |
| 6 | Monte-Carlo method. Central limit theorem | 5.1 |
| 7 | Proof of Central limit theorem. Weak time discretization error | 5.2 |
| 8 | Lax equivalence theorem. Stability of numerical discretization of ODE | 6.2 |
| 9 | Stability of numerical discretization of the heat equation. Computational complexity of Monte Carlo and finite difference methods. | 6.2 |
| 10 | Markov chains and dynamic programming. Control variates | 8.1-8.5 |
| 11 | American options | 6.1 |
| 12 | Optimal control problems | 9.1-9.1.6, 9.3-9.3.2 |
Written exam
The questions on the exam will be a subset of the following list of questions, i.e. all the questions on the exam will be taken from the list. The list is now complete. No more questions will be added.
Since the questions are given before the exam the grading will be strict. Rote learning is not recommended. If the theory and proofs have not been fully understood, often errors will creep in, that will lead to reductions of the number of points awarded.
Re-exam
The re-exam will take place Tuesday August 23, 2016, at 9-13, in seminar room 3418 at the department of Mathematics, KTH. To go there, walk down the stairs from the Mathematics student expedition.