A framework for modeling clustering in natural hazard catastrophe risk management and the implications for re/insurance loss perspectives

In this paper, we present a novel framework for modelling clustering in natural hazard risk models. The framework we present is founded on physical principles where large-scale oscillations in the physical system is the source of non-Poissonian (clustered) frequency behaviour. We focus on a particular mathematical implementation of the "Super-Cluster" methodology that we introduce. This mathematical framework has a number of advantages including tunability to the problem at hand, as well as the ability to model cross-event correlation. Using European windstorm data as an example, we provide evidence that historical data show strong evidence of clustering. We then develop Poisson and clustered simulation models for the data, demonstrating clearly the superiority of the clustered model which we have implemented using the Poisson-Mixtures approach. We then discuss the implications of including clustering in models of prices on catXL contracts, one of the most commonly used mechanisms for transferring risk between primary insurers and reinsurers. This paper provides a number of new insights into the impact clustering has on modelled catXL contract prices. The simple model presented in this paper provides an insightful starting point for practicioners of natural hazard risk modelling.