# NMAA05070U Basic Non-Life Insurance Mathematics (Skade1)

Volume 2024/2025
Education

BSc Programme in Actuarial Mathematics

Content

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.

Competences:

• 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

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

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

Open book, but no electronic aids are allowed.

Marking scale