Ein neuer Ansatz zur Frequenzmodellierung im Versicherungswesen (A new Approach to frequency modeling in risk theory)

TL;DR

This paper introduces a novel approach to modeling claim frequencies in insurance risk theory using random proportions of contracts, offering improved fit and a new goodness-of-fit testing method.

Contribution

It proposes a new frequency modeling approach based on random proportions, enhancing flexibility and fit over traditional discrete distributions.

Findings

New model fits claim frequency data better than classical distributions

Enables statistical goodness-of-fit testing with quantile-quantile plots

Applicable to both claim frequency and size distributions

Abstract

The collective risk model differentiates usually between claims frequencies (and their distribution) and claim sizes (and their distribution). For the claims frequencies typically classical discrete distributions are considered, such as Binomial-, Negative binomial- or Poisson distributions. Since these distributions sometimes do not really fit to the data we propose a different approach here for claim frequencies via random proportions of the number of insurance contracts. This approach also allows for a statistical goodness-of-fit test via quantile-quantile-plots and can likewise be applied to the modelling of claim size distributions.