Abstract
Abstract. In this paper, we present a conceptual framework for modelling clustered natural hazards that makes use of historical event data as a starting point. We review a methodology for modelling clustered natural hazard processes called Poisson mixtures. This methodology is suited to the application we have in mind as it naturally models processes that yield cross-event correlation (unlike homogeneous Poisson models), has a high degree of tunability to the problem at hand and is analytically tractable. Using European windstorm data as an example, we provide evidence that the 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 mixture approach. We then discuss the implications of including clustering in models of prices of catXL contracts, one of the most commonly used mechanisms for transferring risk between primary insurers and reinsurers. This paper provides a number of unique insights into the impact clustering has on modelled catXL contract prices. The simple modelling example in this paper provides a clear and insightful starting point for practitioners tackling more complex natural hazard risk problems.
Highlights
The broad subject of interest in this paper is natural hazard catastrophe risk modelling
We summarize a number of key points that we would like to emphasize related to using Poisson mixtures for modelling clustered phenomena: 1. Using the results in Wang (1998), Appendix A provides the expression for the probability generating function consistent with the Poisson mixture framework
We provide a simple conceptual framework for building a clustered model and review the properties of a Poisson mixture formulation of this framework
Summary
The broad subject of interest in this paper is natural hazard catastrophe risk modelling. The timeline simulation of financial loss on a primary insurance company portfolio is used to model the price of contracts used to transfer risk to reinsurers (which provide insurance for primary insurance companies). S. Khare et al.: Framework for modelling clustering explain by European windstorm models that are based on the Poisson assumption, as we will show in this paper. 4, we provide new insights into the impact that modelling clustering has on so-called catastrophe excess of loss contracts, which is one of the important mechanisms for transferring risk between primary insurers and reinsurers. These insights are developed using numerical simulations and to a certain degree analytic theory.
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