Program Overview

Program Overview

The MSc Programme in Actuarial Mathematics offers a course in Applied Probability, which develops techniques for stochastic modeling. This course utilizes concepts and tools from Markov processes, renewal theory, random walks, and optionally, themes like Markov additive processes and regeneration.

Course Description

Applied Probability is an area that develops techniques for the use in stochastic modeling. The course covers the class of phase-type distributions, defined in terms of absorption times in Markov processes, which play a major role throughout the course. These distributions constitute a class that may approximate any positive distribution arbitrarily close and provide elegant solutions to complex problems by using probabilistic arguments often relying on sample path arguments and leading to explicit formulae expressed in terms of matrices.

Learning Outcomes

At the end of the course, the student is expected to have:

• The ability to employ classical tools from Applied Probability for solving stochastic models by performing probabilistic (sample path) arguments.
• Knowledge about renewal theory, random walks, Markov processes, phase-type distributions, ladder height distributions, ruin probabilities, severity of ruin, and heavy-tailed modeling of extremal events.
• Skills to formalize phase-type distributions and their transformed counterparts, discuss their theoretical background, and apply them in the modeling of risk and extremal events.
• Competences to identify patterns of random phenomena and build adequate stochastic models that can be solved for by using Markov processes and related techniques.

Literature

The course uses the textbook "Matrix-exponential distributions in Applied Probability" by M. Bladt & B. F. Nielsen (2017), published by Springer Verlag.

Academic Qualifications

Recommended academic qualifications include probability theory at the bachelor's level, including measure theory. Some previous exposure to stochastic processes will be an advantage. Academic qualifications equivalent to a BSc degree are recommended.

Teaching and Learning Methods

The course consists of 7 weeks of lectures (2 x 2 hours per week) combined with theoretical and practical exercises (2 hours per week).

Workload

The workload is distributed as follows:

• Lectures: 28 hours
• Preparation: 163 hours
• Exercises: 14 hours
• Exam: 1 hour
• Total: 206 hours

Exam

The exam is an oral examination with 30 minutes of preparation, and all aids are allowed during preparation. The marking scale is a 7-point grading scale, and there is no external censorship.

Course Information

• Language: English
• Course code: NMAK19003U
• Credit: 7.5 ECTS
• Level: Full Degree Master
• Duration: 1 block
• Placement: Block 3
• Schedule: C
• Course capacity: No limit
• Study board: Study Board of Mathematics and Computer Science
• Contracting department: Department of Mathematical Sciences
• Contracting faculty: Faculty of Science
• Course Coordinators: Mogens Bladt
• Lecturers: Mogens Bladt

Additional Information

The course is self-contained, providing all necessary background from both theory, applications, and estimation. Students who come across topics they have encountered previously will benefit from reviewing the material in this alternative and highly probabilistic context, enabling a deeper understanding of the underlying subjects. The fitting of phase-type and/or their heavy-tailed counterpart to data will also be considered, as this constitutes an important part of their applicability.