Nada

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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 !
Push here to fill in the course inquiry:
Kursanalys : Results from the evaluation of the course given in 2002 (Swedish)

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Senast ändrad 15 maj 2006
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