Modeling lower-truncated and right-censored insurance claims with an extension of the MBBEFD class

TL;DR

This paper extends the MBBEFD distribution class to better model lower-truncated and right-censored insurance claims, addressing limitations of classical models and analyzing the impact of policy changes.

Contribution

It introduces an extended family of MBBEFD distributions suitable for insurance claims with truncation and censoring, bridging gaps between reinsurance and insurance modeling.

Findings

The extended MBBEFD class can model both unimodal skewed and monotonically decreasing densities.

The new family accommodates lower truncation and right censoring in claims data.

Changes in deductibles and coverage limits influence the distribution choice and parameters.

Abstract

In general insurance, claims are often lower-truncated and right-censored because insurance contracts may involve deductibles and maximal covers. Most classical statistical models are not (directly) suited to model lower-truncated and right-censored claims. A surprisingly flexible family of distributions that can cope with lower-truncated and right-censored claims is the class of MBBEFD distributions that originally has been introduced by Bernegger (1997) for reinsurance pricing, but which has not gained much attention outside the reinsurance literature. Interestingly, in general insurance, we mainly rely on unimodal skewed densities, whereas the reinsurance literature typically proposes monotonically decreasing densities within the MBBEFD class. We show that this class contains both types of densities, and we extend it to a bigger family of distribution functions suitable for modeling lower-truncated and right-censored claims. In addition, we discuss how changes in the deductible or the maximal cover affect the chosen distributions.