NMAK18000U An Introduction to Large Deviations

Volume 2026/2027
Education

MSc Programme in Actuarial Mathematics

MSc Programme in Statistics 

Content

Large deviations theory has played an important role in applied probability, beginning with the early work of Harald Cramer in ruin theory, and extending to many modern topics arising, e.g., in rare event simulation and statistics.  This will be an introductory course in the theory and applications of large deviation methods.  Topics will include:  Cramer's theorem for sample means and for ruin problems in one and higher dimensions; Sanov's theorem for empirical measures; path properties; and contemporary statistical applications related to Bahadur efficiency for minimum divergence measures.  Throughout the course, emphasis will be given on understanding the key results and their connection to various applications in insurance, finance, statistics, and efficient Monte Carlo simulation.

 

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 standard Cramer theorems (for sample means and ruin problems), including basic multidimensional problems, and applications of the theory to empirical measures and paths of stochastic processes.  The student should also understand certain natural applications to importance sampling, insurance and finance, and statistics.

Introductory course in measure-theoretic probability theory (e.g., Sand2 or equivalent).

Academic qualifications equivalent to a BSc degree is recommended.
4 hours of lecture per week for 7 weeks
  • Category
  • Hours
  • Lectures
  • 28
  • Preparation
  • 177
  • Exam
  • 1
  • Total
  • 206
Written
Feedback by final exam (In addition to the grade)
Credit
7,5 ECTS
Type of assessment
Oral examination, 30 minutes
Type of assessment details
30-minute oral exam without aids and without preparation.
Examination prerequisites

To participate in the exam the two compulsory assignments must be approved and valid.

Aid
No aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examinators.
Re-exam

Same as the ordinary exam.

 If the compulsory assignments were not approved before the ordinary exam they must be (re)submitted and approved. They must be (re)submitted at the latest three weeks before the beginning of the re-exam week.

Criteria for exam assesment

The student must in a satisfactory way demonstrate that they have mastered the learning outcome of the course.