Contents |
Course Title
Actuarial Risk Theory
Course Code
IAM 746
Credit
(3-0)3
Prerequisites
Consent of the Instructor.
Content
Basic concepts of probability in connection with Risk Theory; introduction to risk processes (claim number process, claim amount process, total claim number process, total claim amount process, inter-occurance process); convolution and mixed type distributions; risk models (individual and collective risk models); numerical methods ( simple methods for discrete distributions, Edgeworth approximation, Esscher approximation, normal power approximation); premium calculation principles; Credibility Theory; retentions and reinsurance; Ruin Theory; ordering of risks.
Aims
The aim of this course is to give the fundamental concepts of actuarial risk theory and to teach the role of statistics on actuarial concepts and the methods optimal decision and management in insurance.
Outline
- Week 1-2. Basic concepts of probability in sense of risk theory.
- Week 3 Introduction to risk processes (claim number process, claim amount process, total claim number process, total claim amount process, inter-occurance process)
- Week 4 Convolution and mixed type distributions
- Week 5-6 Risk models ( individual and collective risk models)
- Week 7-8 Numerical methods ( simple methods for discrete distributions, Edgeworth approximation, Esscher approximation, normal power approximation)
- Week 9-10 Premium calculation principles
- Week 11 Credibility Theory
- Week 12 Retentions and reinsurance
- Week 13 Ruin theory
- Week 14 Ordering of risks
Learning Outcomes
The course will provide basic knowledge for advanced actuarial techniques. After taking the course, the students will have obtained a certain amount of knowledge on Actuarial Risk Theory which they may use in their future research activities. Suggested Textbooks: Course notes H. Bühlmann, Mathematical Methods in Risk Theory, Springer-Verlag (1970) W.R. Heilmann, Fundamentals of Risk Theory, (1988) R. Kaas, M.J. Goovaerts, J. Dhaene, M. Denuit, Modern Actuarial Risk Theory, Kluwer Academic Publisher, (2001)