Syllabus

Math 595, CRN 53563, Section LD
Large Deviations

The study of atypical or rare events occupies an important part in many probabilistic analyses. While there are many types of rare events, the theory of exponentially small events appears frequently enough that it deserves special consideration. We will explore the circle of ideas known as large deviations, which studies the structure and transformations of such exponentially small events. We will attempt, when possible, to connect this theory to financial problems, following some ideas of Pham; rare events are an important part of the financial landscape, not only as cases of extreme risk, but also as an integral part of investment-grade securities which, by definition, should suffer losses only rarely. There will be a lot of homework. I will ask you to prove a number of elementary results and simplified calculations. The lectures will focus on things which introduce what is new. The class runs until October 16.

Provisional Schedule
References:
Grading: Grades will be determined on the basis of homework (30%), a midterm (35%) and a final (35%). I will attempt announce relevant things on my Twitter Feed.

Richard Sowers (Home Page)

Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W Green St.
Urbana, IL 61801
r-sowers@math.uiuc.edu (217) 333-6246