NMAK19003U  Applied Probability

Volume 2019/2020

MSc Programme in Actuarial Mathematics 


Applied Probability is an area which develops techniques for the use in stochastic modelling. In this course we introduce some of the classical comcepts and tools like Markov chains and processes, renewal theory, random walks and optionally themes like Markov additive processes and regeneration. 

With the use of phase-type distribution we provide a number of specific examples, which may be taken from the areas of insurance risk, queueing theory, reliability theory or population genetics. 

Phase-type distributions is a renowned class of distributions in Applied Probability, which allows for elegant solutions to complex problems through probabilistic arguments often relying sample path arguments. We shall be providing a thourough treatment of phase--type distributions, their properties and optionally their estimation. 

The course is self-contained and will provide all the necessary background on stochastic processes which is needed. 

Learning Outcome


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

Knowledge about renewal theory, random walks, Markov processes, phase-type distributions, matrix-exponential distributions, ladder height distributions, ruin probabilities, severity of ruin, waiting time distributions in queues, lifetime distributions in reliability theory.

Skills to formalize phase-type distributions, discuss their theoretical background, and apply them in insurance theory, queueing theory or reliability theory.

Competences to idenitify patterns of random phenomena and building adequate stochastic models which can be solved for by using Markov processes and related techniques.


M. Bladt & B. F. Nielsen (2017) Matrix-exponential distributions in Applied Probability. Springer Verlag. 

Probability theory at bachelors level, including measure theory.

Academic qualifications equivalent to a BSc degree is recommended.
9 weeks teaching consisting of lectures (2 x 2 hours per week) combined with theoretical and practical exercises (4 hours per week). The students are expected to prepare for lectures and exercise sessions (approx. 4 hours per week on average) and work independently in study groups (approx. 8 hours per week on average).
Continuous feedback during the course of the semester
7,5 ECTS
Type of assessment
Oral examination, 30 min.
Oral examination with 30 min. preparation.
All aids allowed
Marking scale
7-point grading scale
Censorship form
No external censorship
Several internal examiners.

The same as the ordinary exam.

Criteria for exam assesment

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

  • Category
  • Hours
  • Lectures
  • 36
  • Exercises
  • 27
  • Preparation
  • 142
  • Exam
  • 1
  • Total
  • 206