|
The aim of the course is to introduce basic theories and
methods in stochastic calculus for applications in stochastic
control & optimization, financial mathematics and signal theory.
Prerequisities:
SF2940 Probability Theory or equivalent course.
Administration:
Questions concerning registration for the course and other administrative matters should be addressed to the student affairs office.
The homepage for the student affairs office can be reached via the following links:
Swedish
English
Examination:
There will be a written exam on Wednesday March 15, 2018, 08.00-13.00.
The exams are closed book with no aids allowed. Please note that you are not allowed to bring calculators, cell phones, tablets, smart watches, or any other electronic devices to the examination desk, even if the devices are turned off.
Students requiring support during the exams should contact KTH FUNKA in advance.
Grades are set according to the quality of the written exam.
Grades are given in the range A-F, where A is the best and F means
failed, and Fx.
Fx means that you have the right to a complementary examination
(to reach the grade E).
The criteria for Fx is a grade F on the exam, and that an isolated part
of the course can be
identified where you have shown a particular lack of
knowledge and that the examination after a complementary examination on
this
part can be given the grade E.
A written re-exam will be given on Friday June 8, 2018, 14.00-19.00.
Homework:
There will be two homework assignments. Note that solving the homework
assignments is NOT a requirement for passing the course. You must work
individually. Correctly solved homework assignments handed in on time will result in that you will not have to solve parts of, or the whole of the first exercise on the exam in March and the re-exam (in June), but after that you either have to re-do the homework or solve all exercises at the exam.
Course literature:
Boualem Djehiche: Stochastic Calculus. An Introduction with
Applications.
Available from "THS Kårbokhandel", Drottning Kristinas väg 15-19.
Extra material about stochastic optimal control will be handed out.
Preliminary plan
(CL=Camilla Landen, MF=Martina Favero)
| Day |
Date |
Time |
Place |
Topic |
Lecturer |
| Tue |
16/1 |
13-15 |
U21
|
Integration and probability theory
|
CL |
| Wed |
17/1 |
15-17 |
U21
|
Conditional expectation
|
CL |
| Thu |
18/1 |
15-17 |
U21
|
Martingales in discrete time
|
CL |
| Mon |
22/1 |
10-12 |
U21
|
Optional stopping and stopping times
|
CL |
| Tue |
23/1 |
13-15 |
U41
|
Stochastic integrals in discrete time
|
CL |
| Wed |
24/1 |
15-17 |
U21
|
Exercise
|
MF |
| Thu |
25/1 |
15-17 |
U21
|
Discrete Brownian motion
|
CL |
| Mon |
29/1 |
10-12 |
U21
|
Girsanov's theorem
|
CL |
| Tue |
30/1 |
13-15 |
U21
|
Martingales in continuous time
|
CL |
| Wed |
31/1 |
15-17 |
U21
|
Exercise
|
MF |
| Thu |
1/2 |
15-17 |
U21
|
Brownian motion
|
CL |
| Mon |
5/2 |
10-12 |
U21
|
Ito integrals
|
CL |
| Tue |
6/2 |
13-15 |
U21
|
Ito's formula and applications
|
CL |
| Wed |
7/2 |
15-17 |
U31
|
Exercise
|
MF |
| Thu |
8/2 |
15-17 |
U21
|
Stochastic differential equations
|
CL |
| Mon |
12/2 |
10-12 |
U21
|
Diffusion processes
|
CL |
| Tue |
13/2 |
13-15 |
U41
|
Martingale representation
|
CL |
| Thu |
15/2 |
15-17 |
U21
|
Exercise
|
MF |
| Mon |
19/2 |
10-12 |
U21
|
Optional stopping and stopping times
|
CL |
| Tue |
20/2 |
13-15 |
U21
|
Stochastic control
|
CL |
| Thu |
22/2 |
15-17 |
U21
|
Exercise
|
MF |
| Mon |
26/2 |
10-12 |
U21
|
Stochastic control
|
CL |
| Tue |
27/2 |
13-15 |
U21
|
Stochastic control
|
CL |
| Thu |
1/3 |
15-17 |
U21
|
Exercise
|
MF |
Welcome, we hope you will enjoy the course!
Camilla and Martina
To course
web page
|
