From 2015.09.14 to 2016.01.04
Monday: 14-15:40
Wednesday: 10-12
Place: Chen Ruiqiu Building, room 107
Office hour: Wednesday from 13:00 to 15:30
Office: Math building, room 2.105
Teaching Assistant: Zhang Yaoyuan volwc@sjtu.edu.cn
This lecture is an introduction to the theory of stochastic processes, with a special focus on Martingale Theory. The discrete time framework is first addressed and then the continuous time with the construction of Ito’s integral. One finally address with the help of Ito’s Formula some Stochastic differential equations. Throughout the whole course we illustrate the theory by means of examples within financial mathematics.
You can ask for hints to the teaching assistant or myself during office hours.
Measure theory, topology, some basics of functional analysis, and probability theory.
The course won’t follow any textbook however you might find some interesting/alternative approaches in
For measure and integration theory:
[1] “Measure and Integration Theory”, H. Bauer, 2001 (very complete)
For stochastic processes:
[2] “Foundation of Modern Probability”, O. Kallenberg, 2nd Edition 2002 (very general but complete)
[3] “Stochastic Calculus and Financial Applications”, J.M. Steel, 2000 (easy but complete introduction with applications to finance)
[4] “Probability and Potentials B”, P. Dellacherie, P.A. Meyer, 1982 (the most general reference, very hard and build upon Probability and Potentials A)
Disclaimer: The following lecture notes are meant to be a script for the students attending the lecture. Since they are written on the fly, they change quite often are prone to typos or some mistakes that are corrected as the lecture advance. So if you are not a student of my class, I suggest that you take it with precaution or wait until the lecture is finished so that the lecture notes converges to an acceptable steady state.