Kurs stodif12 [NADA, KTH]

DN2281 Computational Methods for Stochastic Differential Equations, spring 2012

7.5 Credits

Formal description, that is, the text on the student web.

Most recent changes on 30 June 2012.

Re-exam

The re-exam will take place on Friday August 24, at 13-17, in seminar room 4523, Lindstedtsvägen 3, floor 5.

News

The written May 29 exam has been corrected. You can pick it up at studentexpeditionen. They are open between 10 and 11 each day until Friday June 29.

The deadline for homework 4 has been extended to the lecture Tuesday April 17. Note, however that the deadline for homework 5 is still the lecture Tuesday April 24.

Homework 4 is now (April 3) changed slightly, so that the initial condition for S is given.

Course Questionnaire

Teaching and Examination

The first lecture is held January 17 in room D42. Examination is by homework, presentation, and a final written exam. The homework and presentations are carried out by groups of students. Each group hand in a report on each assignment.

Teacher

Mattias Sandberg, room 4525, CSC, Lindstedtsvägen 3, floor 5. Telephone: 08-790 7783. E-mail: msandb(at)kth.se

Office Hours

Fridays 15-16. If you want to meet me at another time it is safest to make an appointment in advance via e-mail.

General Description and Aim

We will define what is meant by stochastic differential equations and their solutions. The definition uses numerical schemes, and in the process we also obtain convergence results for these schemes. Expected values as functions of starting positions for SDEs are given by solutions to partial differential equations. We will consider the two different possibilities of finding such expected values by Monte Carlo simulation and finite difference schemes.

Applications are e.g. finance, where stock prices are modelled using SDEs, and molecular dynamics, where SDEs are used to model e.g. systems with constant temperature.

Optimal control will also be discussed in the course. It is needed e.g. in the optimal hedging problem of optimizing a portfolio.

Exam Paper

A substantial part of the exam will be based on the following list of questions.

Literature

We will use the lecture notes, by Jesper Carlsson, Kyong-Sook Moon, Anders Szepessy, Raul Tempone, and Georgios Zouraris.

Homework

Homework 1 on Ito integrals, due the lecture Tuesday January 31.
Homework 2 on Ito and Stratonovich, due the lecture Friday February 24.
Homework 3 on Feynman-Kac and Options, due the lecture Tuesday March 20.
Homework 4 on Monte Carlo and Options, due the lecture Tuesday April 17.
Homework 5 on dynamic programming, due the lecture Tuesday April 24.

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