NMAA05070U Basic Non-Life Insurance Mathematics (Skade1)

Volume 2024/2025

BSc Programme in Actuarial Mathematics


The course will give an overview of some important elements of non-life insurance and reinsurance:

Models for claim numbers: the Poisson, mixed Poisson and renewal process.
Stochastic models for non-life insurance risks, in particular the compound Poisson, compound mixed Poisson and renewal models.
Large and small claims distributions.
Premium calculation principles for the total claim amount of a portfolio.
Experience rating: calculation of the premium in a policy.
Bayes estimation and credibility theory.

Learning Outcome

At the end of the course, the students are expected to have the following knowledge:

  • Definition and properties of claim number processes; in particular Poisson processes, mixed Poisson processes and renewal processes.
  • Definition and properties of total claim amount processes in a portfolio.
  • The Cramer-Lundberg and the renewal model as basic risk models.
  • Methods for approximating the distribution of risk models.
  • Small and large claim distributions and their properties.
  • Premium calculation principles and their properties.
  • Reinsurance treaties and their properties.
  • Bayesian methods in a non-life insurance context, in particular the
  • Bayes and linear Bayes estimators for calculating the premium in a policy.

The student will gain the following skills:

  • Calculation of distributional characteristics of
  • the claim number and total claim amount processes, in particular their moments.
  • Calculation of premiums for a non-life (re)insurance portfolio  and a non-life individual policy.
  • Statistical skills for analysizing  small and large claim data. 
  • Risk analyses  in a non-life portfolio.
  • Proficiency in Bayesian methods in a non-life insurance context.


  • At the end of the course, the student  will be able to relate and illustrate theory and practice in a non-life insurance company.
  • The student will be able to read the actuarial non-life literature and be operational in premium calculation and risk analysis.

Examples on course literature:

T. Mikosch. Non-Life Insurance Mathematics.

An Introduction with the Poisson Process.

2nd edition, Springer 2009

Basic knowledge of probability theory, statistics and stochastic processes:

Sandsynlighedsteori (Sand2) - alternatively Mål- og integralteori (MI) from previous years. Forsikring og jura 1 (Forsik&Jura1) or similar courses.
5 hours of lectures and 3 hours of exercises per week for 7 weeks.
  • Category
  • Hours
  • Lectures
  • 35
  • Preparation
  • 147
  • Theory exercises
  • 21
  • Exam
  • 3
  • Total
  • 206

Oral feedback will be given to the students’ presentations in class.

7,5 ECTS
Type of assessment
On-site written exam, 3 hours under invigilation
Written aids allowed

Open book, but no electronic aids are allowed.


Marking scale
7-point grading scale
Censorship form
External censorship

30 minutes oral examination with no preparation and no aids.

Criteria for exam assesment

The student should convincingly and accurately demonstrate the knowledge, skills and competences described under Intended learning outcome.