An Alternative to GLM for Including Covariates in Loss Models with Application to Operational Risk Modeling

• Activity Number: 442
• Type: Topic Contributed
• Date/Time: Wednesday, August 6, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Steven Major*+ and Jacques Rioux
• Companies: SAS Institute and SAS Institute
• Keywords: GLM ; Loss Models ; Scale Parameter ; Truncation ; Censoring

Abstract

In recent years, the use of GLM in the insurance industry for ratemaking and stochastic reserve calculation has been staggering. The GLM machinery is powerful and attractive in its simplicity, but practitioners often overlook data limitations that are incompatible with the model at hand in order to employ the method. Limitations such as truncated or censored data are too often forgotten in order to be able to put the square peg of the data into the round hole of GLM. We introduce an alternative model that is fundamentally hierarchical to incorporate the effect of the covariates into a scale parameter. The fitting method we use is complete maximum likelihood. We compare the model and method with the GLM approach and give examples of application on insurance loss data and in operational loss risk analysis. We describe practical ways to initialize parameters for fitting and we also present ways of judging goodness of fit and model selection. The advantage of the method is that it can be applied to a much more general class of models, the only requirement being that its parameterization includes a scale parameter.