An Introduction to Large Deviations

Course content

This will be an introductory course in the theory of large deviations and its applications.  Topics will include:  Cramer's theorem for sample means and for level crossings, moderate deviations, heavy tails, and a brief introduction to the multidimensional theory.  Applications will include insurance mathematics and finance, statistics, and Monte Carlo methods (importance sampling).

 

Education

MSc Programme in Actuarial Mathematics

MSc Programme in Statistics 

Learning outcome

Knowledge:  By the end of the course, the student should develop an understanding of the basic principles of large deviations and some of its applications.

Skills:   The student should develop analytical and computational skills for analyzing complex problems using large deviation methods.

Competencies:  The student should develop an understanding of, and be able to apply, the Cramer theorems (and their analogs for moderate deviations and heavy tails), including basic multidimensional problems.  The student should also understand natural applications to importance sampling, insurance and finance, and statistics.

4 hours of lecture per week for 7 weeks

ECTS
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
30 minute oral exam without aids and without preparation.
Aid
Without aids
Marking scale
7-point grading scale
Censorship form
No external censorship
One internal examinator.
Criteria for exam assessment

The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.

Single subject courses (day)

  • Category
  • Hours
  • Preparation
  • 177
  • Exam
  • 1
  • Lectures
  • 28
  • English
  • 206