Upp till *kursens hemsida*.

# Aktuell information om 2D1269, Matematiska modeller, analys och simulering, del 2

## Teachers

Jesper Carlsson, NADA, (jesperc),
Office hour : Tuesdays 13.00-14.00, room 1526

Erik von Schwerin, NADA, (schwerin),
Office hour : Thursdays 10.00-11.00, room 4520

Anders Szepessy, NADA, (szepessy)

All addresses are at nada.kth.se

## Course material

- lecture notes

- notes on variance reduction,

- a Fourier wavelet method for SPDE,

## Lecture and Homework Schedule

In room 4523 at NADA, starting Friday January week 3, 2006
Lectures: Fridays 10-12 period 3 and 4.
Exercise and presentations: Tuesday 15-17 period 3, and Mondays 10-12 period 4

The course focus on the following
*real-world problems* and
mathematical and numerical methods to solve them.
In each application we study relevant mathematical and numerical methods
to solve the problem. This includes
methods and theory for ordinary, partial and stochastic
differential equations, and optimal control, treating
e.g. weak and strong approximation, adaptive numerical methods,
the finite element method, Monte Carlo methods
Week Problem Subject
3,4,5 Population growth with noise Stochastic DE, Ito-calculus,
stocks with noise Euler method,
molecular dynamics weak and strong convergence
6,7,8,9 Option price The Feynman-Kac formula,
American options Monte-Carlo Methods, variance reduction,
finite difference and finite element methods.
11,12,13 Optimal hedging Calculus of Variations, Optimal Control
dynamical programming, Hamilton-Jacobi
equations
14,16,17 Implied volatility Inverse problems, optimal control
reaction rates
18,19 geophysical flow,
turbulent diffusion Convection-diffusion equations, wavelets
Ground water flow correlated noise
material science

## Homework, Computer Lab's , Presentations and Examination

The Examination consists of three parts: Homework problems,
oral presentations and a written exam.
The homework problems will
be available here on the course www-page.
The homework and the presentations are
carried out by *groups of students*.
Each group hand in a report on each assignment.

Homework 1 (pdf) ps on Ito integrals, due week 4.

Homework 2 (pdf) ps on Ito and Stratonovich, due week 5.

Homework 3 (pdf) ps on Feynman-Kac and Options, due week 7.

Homework 4 (pdf) ps on Monte Carlo for Options, due week 9 (Tuesday).

Homework 5 (pdf) ps on Dynamic Programming, due week 14 (Tuesday).

Suggestions ps
for presentation of the computational problems on week 19.

Suggestions for the homework. (Swedish)

## Handout materials for the lectures

An introductory article on numerical simulation of SDE:s by Desmond J. Higham. (Available from the KTH-domain).

The source files for the examples in the article are available here.

Additional sources from Jesper's page.

Example matlab code for example 5.13 used in
exercise session Tuesday week 9.
## Participants and Result

Here is the list of
participants and result of this course.

## Exam Paper

A substantial part of
the exam will be based on a list of questions given

for 2006 here

The maximal score will be 60, and to pass the course you must obtain a total
score, homework included, of approximately 60.
The homework and the presentation
gives maximal 40 credits together, with maximal 5 credits for each homework
and maximal 10 credits for the computational problem.
## Exam

The exam will be held Wednesday May 24:th, 8.00-13.00, in room 4523.
## Student's comments

The course will be evaluated at the end when you will be asked to fill
in a standard course evaluation form, but any comments along the way
are most welcome !
Kursanalys : Results from the evaluation of the course given in 2002 (Swedish)
Upp till *kursens hemsida*.

Sidansvarig: <szepessy@nada.kth.se>

Senast ändrad 15 maj 2006

Tekniskt stöd: <webmaster@nada.kth.se>