Basic Non-Life Insurance Mathematics (Skade1)
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.
BSc Programme in Actuarial Mathematics
At the end of the course, the students are expected to have the
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.
He/she will be able to read the actuarial non-life literature and be operational in premium calculation and risk analysis.
5 hours of lectures and 3 hours of exercises per week for 7 weeks.
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
Stokastiske processer (Stok),
Sandsynlighedsteori (Sand) - alternatively Mål- og integralteori (MI) from previous years.
Forsikring og jura 1 (Forsik&Jura1)
Stochastic processes 2 - no later than at the same time,
or similar courses.
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).
- 7,5 ECTS
- Type of assessment
Written examination, 3 hours under invigilation...
- Written aids allowed
No electronic aids are allowed.
- Marking scale
- 7-point grading scale
- Censorship form
- External censorship
Criteria for exam assessment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.
Single subject courses (day)
- Theory exercises
- Course number
- 7,5 ECTS
- Programme level
- Block 2
- No limit
- Study Board of Mathematics and Computer Science
- Department of Mathematical Sciences
- Faculty of Science
- Thomas Valentin Mikosch (7-726e707478686d457266796d33707a336970)
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Courseinformation of students