NMAA05070U Basic Non-Life Insurance Mathematics (Skade1)

Volume 2013/2014
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,
compund mixed Poisson  and renewal models
Large and small claim distributions
Premium calculation principles for the total claim amount of a portfolio
Ruin probability
Experience rating: calculation of the premium for a policy
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.
Bounds for ruin probabilities of risk processes.
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.
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. (An1, Stok, MI and Forsik&Jura1 or similar courses).
5 hours of lectures and 3 hours of exercises per week for 7 weeks.
  • Category
  • Hours
  • Exam
  • 3
  • Lectures
  • 35
  • Preparation
  • 147
  • Theory exercises
  • 21
  • Total
  • 206
Credit
7,5 ECTS
Type of assessment
Written examination, 3 hours under invigilation
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Aid
All aids allowed
Marking scale
7-point grading scale
Censorship form
External censorship
Re-exam
30 minutes oral examination with 30 minutes preparation. During the preparation time all written aids are allowed. During the examination the student is allowed to consult a short note taken during the preparation time
Criteria for exam assesment
The student must in a satisfactory way demonstrate that he/she has mastered the learning outcome of the course.