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 ruin problems in one and higher dimensions; Sanov's theorem for empirical measures; and large deviations results describing the path properties of stochastic processes. Some emphasis will be given on connecting these results to applications in insurance, finance, statistics, and efficient Monte Carlo simulation methods.
MSc Programme in Actuarial Mathematics
MSc Programme in Statistics
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 natural applications to importance sampling, insurance and finance, and statistics.
4 hours of lecture per week for 7 weeks
Introductory course in measure-theoretic probability theory
(e.g., Sand2 or equivalent).
Academic qualifications equivalent to a BSc degree is
recommended.
- ECTS
- 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 assessment
The student must in a satisfactory way demonstrate that they have mastered the learning outcome of the course.
Single subject courses (day)
- Category
- Hours
- Lectures
- 28
- Preparation
- 177
- Exam
- 1
- English
- 206
Kursusinformation
- Language
- English
- Course number
- NMAK18000U
- ECTS
- 7,5 ECTS
- Programme level
- Full Degree Master
- Duration
-
1 block
- Placement
- Block 1
- Schedulegroup
-
C
- Capacity
- No restrictions/no limitation
- Studyboard
- Study Board of Mathematics and Computer Science
Contracting department
- Department of Mathematical Sciences
Contracting faculty
- Faculty of Science
Course Coordinator
- Jeffrey F. Collamore (9-65716e6e636f717467426f63766a306d7730666d)
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