Distribution Models for Damage Ratios in Vulnerability Modules of Catastrophe Models

In the (re)insurance industry, catastrophe models are used to estimate the frequency of aggregate event losses (loss occurrence) from natural catastrophes (NatCat). These models simulate the loss for every considered single risk (e.g., a building) per stochastic event as the product of its replacement value and a simulated damage ratio (loss ratio) before insurance conditions can be considered. Therefore, distribution models of the random damage ratio are a crucial component of the vulnerability module, although they have largely remained underexplored. We address this gap by reviewing existing models and proposing a novel approach. For this purpose, we establish criteria and essential properties for a vulnerability and distribution model, such as parsimony and identifiability. The previously applied inflated and transformed beta distributions fail to meet these criteria, as one lacks identifiability while the other exhibits implausible behavior such as abrupt jumps. As a new approach, censored distributions are proposed. We focus on censored normal and beta distributions and demonstrate modeling options using earthquake, storm, and flood data. For the latter, we have statistically validated the distribution model. Details of the distribution model’s implementation in the overall vulnerability model are also explicitly considered.