Course information

News The lecture that was originally scheduled on April 4 has been cancelled.

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.¶

Preliminary course plan (to be extended)

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 Written exam A substantial part of the exam will be based on the following list of questions. The list will be continually extended until it stated here that no more questions will be added.