This course is an introduction to stochastic calculus based on the Brownian motion.
Topics include: Introduction of Brownian motion; stochastic integrals; Ito formula and its applications in solving stochastic differential equations.
Textbooks. We will largely follow the required textbook:
• Stochastic differential equations, by B. Øksendal.
Additional references include:
• Introduction to Stochastic Integration, by Hui-Hsiung Kuo.
Grading. The final grade breakdown is as follows: Homework 50%; Midterm 20%;
Final report 30%.
Office hours: Thursday, 10:00 ~ 12:00.
Enclosed please find the lecture notes of this course (September 14, 2015 ~ January 8, 2016).
Week 1st : Introduction of the probability space and martingales
Week 2nd: Ito integrals
Week 3rd: Ito's formula (general version)
Week 4-6th: Continue to prove Ito's formula
Week 7-8th: Applying Ito's formula to prove Burkholder-Davis-Gundy inequalities
Week 9th: The Black–Scholes partial differential equation (BSPDE)
- - - Midterm will be held on November 13 - - -
Week 11-12th: Girsanov's theorem
Week 13th: Applications of Girsanov's theorem
Week 14th: Introduction of Linear Filtering Problems I