In this paper we will show how to set up a practical bonus-malus system with a finite number of classes. We will use the actual claim amount and claims frequency distributions in order to predict the future observed claims frequency when the new bonus-malus system will be in use...

In this paper we study a class of Mixed Bivariate Poisson Distributions by extending the Hofmann Distribution from the univariate case to the bivariate case. We show how to evaluate the bivariate aggregate claims distribution and we fit some insurance portfolios given in the literature...

In this paper we study some bivariate counting distributions that areobtained by the trivariate reduction method...

For the construction of bonus-malus systems, we propose to show how to apply, thanks to simple mathematics, a parametric method encompassing those encountered in the literature...

The adjustment for the cedent's retained risk after excess-of-loss reinsurance with reinstatements is calculated. Therefore we need a multivariate aggregate claims distribution. This distribution is easily given by a multivariate extension of Panjer's recursion. Numerical examples show the...

The adjustment for the cedent's retained risk after excess-of-loss reinsurance with reinstatements is calculated. Therefore we need a multivariate aggregate claims distribution. This distribution is easily given by a multivariate extension of Panjer's recursion. Numerical examples show the...

The Kolmogorov distance is used to transform arithmetic severities intoequispaced arithmetic severities in order to reduce the number ofcalculations when using algorithms like Panjer's formulae for compounddistributions...