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.
Intended learning outcomes:
To pass the course, the student should be able to do the following:
To receive the highest grade, the student should in addition be able to do the following:
SF 2940 Probability Theory or equivalent course.
The written exam is on Thursday March 16, 2016, 14.00-19.00.
The written re-exam is on on Friday June 9, 2016, 14.00-19.00.
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.
The exams are closed book with no aids allowed.
Students requiring assistance during the exams should contact KTH FUNKA in advance.
There will be two homework assignments. Note that solving the homework assignments is not a requirement for passing the course. 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.
This course is structured in three learning units (learning cycles). Each unit consists of 4-5 lectures, 2 exercise sessions and 1 repetition session. Content of the units:
Learning Unit I: Conditional expectation, martingales and stochastic integrals in discrete time, Girsanov Theorem.
Learning Unit II: Martingales in continuous time, Brownian motion, Ito integral and Ito Lemma.
Learning Unit III: Martingale Representation Theorem, stochastic differentiable equations, Ito diffusions, Kolmogorov equations, Feynman-Kac formula.
A list with further literature is found here.
Preliminary plan (KS=Kevin Schnelli, MF=Martina Favero)
|Published by: Kevin Schnelli