Estimating the real-time case fatality rate of COVID-19 using Poisson mixtures model

ABSTRACTWe proposed using Poisson mixtures model that utilized data of deaths, recoveries, and total confirmed cases in each day since the outbreak. We demonstrated that our CFR estimates for Hubei Province and other parts of China were superior to the simple CFR estimators in the early stage of COVID-19 outbreak.

Experience rating with Poisson mixtures

We propose a Poisson mixture model for count data to determine the number of groups in a Group Life insurance portfolio consisting of claim numbers or deaths. We take a non-parametric Bayesian approach to modelling this mixture distribution using a Dirichlet process prior and use reversible jump Markov chain Monte Carlo to estimate the number of components in the mixture. Unlike Haastrup, we show that the assumption of identical heterogeneity for all groups may not hold as 88% of the posterior probability is assigned to models with two or three components, and 11% to models with four or five components, whereas models with one component are never visited. Our major contribution is showing how to account for both model uncertainty and parameter estimation within a single framework.

Modelling clustering of natural hazard phenomena and the effect on re/insurance loss perspectives

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.

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.