Stochastic Differential Equations

MATH8008, Spring semester, 2019

Instructor: Yizao Wang
Email: yizao.wang@uc.edu
Office: 4302 French Hall.
Office Hours: Fri, 2:30-3:30pm, other time by appointment.
Class meeting: MWF 1:25pm - 2:20pm, 816 Swift Hall.

Textbook

• Stochastic Calculus and Financial Applications, Michael Steele. Applications of Mathematics (New York), 45. Springer-Verlag, New York, 2001.
• (recommended) An Introduction to Stochastic Differential Equations, Lawrence Evans. American Mathematical Society, Providence, RI, 2013.
• (recommended) Stochastic Differential Equations. An introduction with applications. Øksendal, Bernt. Sixth edition. Universitext. Springer-Verlag, Berlin, 2003.

Course description

This course covers stochastic calculus and stochastic differential equations. I will spend 1/2 - 2/3 of the semester on stochastic calculus. The lectures for SDEs will be relatively less rigorous. I will follow mostly the excellent textbook by Michael Steele (see above), Chapters 1-4, 6-9, and then cover selected materials from Chapters 10-15, skipping most of financial applications.

Grades

• Grading: there will be 2-3 homework problem sets.

Tentative Schedule

• Week 1 (Jan 14): Chapter 1.
• Week 2 (Jan 21): Chapter 2. No class on MLK, Monday (Jan 21).
• Week 3 (Jan 28): Chapter 3.
• Week 4 (Feb 4): Chapter 4.
• Week 5 (Feb 11):
• Week 6 (Feb 18): Chapter 6.
• Week 7 (Feb 25): Chapter 7.
• Week 8 (Mar 4): Chapter 8.
• Week 9 (Mar 11): Chapter 9.
• Week 10 (Mar 18): Spring Break.
• Week 11 (Mar 25):
• Week 12 (Apr 1):
• Week 13 (Apr 8):
• Week 14 (Apr 15):
• Week 15 (Apr 22):

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