Syllabus
1. Distributions of claim sizes derived by a power transform, generalized and generalized inverse distributional families.
Tail behavior, subexponential distributions. 2. (a,b,0) and (a,b,1) classes of counting distributions. 3. Panjer recursive formula for compound distributions.
Methods of discretization of a continuous claim size distribution. Calculation of a compound distribution by means of FFT.
Approximations of the aggregate loss distribution. 4. Discrete-time ruin theory model. 5.
Pricing of XL-reinsurance with reinstatements. 6. Simple methods of classification ratemaking.
Loglinear model. 7. Mack's model and chain-ladder method.
Bornhuetter-Ferguson method. Poisson model for incremental development triangles.
Annotation
Probabilistic modeling of claim sizes, claim counts and aggregate losses. Application of the collective model in ruin theory and in reinsurance.
Introduction to classification ratemaking. Basic methods of claims reserving.