Advanced actuarial models

The main objective of this mini-course is to study advanced actuarial models in non-life insurance and to introduce some claims reserving methods which are relevant to actuarial practice. The contents covered by this mini-course are the following.
 

1. Distribution of aggregate claims

·         Collective risk model
·         Calculation of aggregate claims distribution
·         Individual risk model versus collective risk model
 

2. Incurred But Not Reported (IBNR) techniques

·         Chain-ladder method
·         Bornhuetter-Ferguson method
·         Bayesian models
·         Distributional models
 

3. Bonus-Malus systems

·         Models for claim counts
·         Construction of an optimal BMS
·         Bonus-Malus scales
·         Other topics (severity, hunger for bonus)
 

4. Claim surplus process (optional)

·         Discrete time risk models
·         Continuous time risk models
 
References:
-          Loss Models, 4th Edition, 2012, by S.A. Klugman, H.H. Panjer and G.E. Willmot, Wiley.
-          An introduction to Mathematical Risk Theory, 1979, by H.U. Gerber, S.S. Huebner Foundation for Insurance, U. of Pennsylvania.
-          Modern Actuarial Risk Theory, 2001, by R. Kass, M. Goovaerts, J. Dhaene and M. Denuit, Kluwer Academic Publishers.
-          Stochastic claims reserving methods in insurance, 2008, by M.V. Wüthrich and M. Merz, John Wiley & Sons, Ltd.
-          Bonus-Malus Systems in Automobile Insurance, 1995, by J. Lemaire, Kluwer Academic Publishers.
Insurance Risk and Ruin, 2005, by D.C.M. Dickson, Cambridge University Press.