# NMAA05070U Basic Non-Life Insurance Mathematics (Skade1)

Volume 2020/2021
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.
He/she 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: Stokastiske processer (Stok), Mål- og integralteori (MI), Forsikring og jura 1 (Forsik&Jura1) and no later than at the same time: Stochastic processes 2 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 on students’ presentations in class.

Feedback by final exam (in addition to the grade): In connection with written exam (oral reexam).

Credit
7,5 ECTS
Type of assessment
Written examination, 3 hours under invigilation
...
Aid
Written aids allowed

No electronic aids are allowed.

Marking scale