Fitting a GLM to Incomplete Development Triangles

When fitting a generalized liner model (GLM) to a development triangle is discussed in the existing actuarial literature, reference is usually made to statistical packages for accomplishing this task. This paper presents a practical discussion of how to use Visual Basic to fit a GLM to a triangle with special emphasis on how to deal with incomplete data. Interested readers can contact the author to request a copy of an MS Excel application that implements the algorithms discussed in this paper. The application of GLMs to incomplete development triangles is motivated by translating judgments of practicing actuaries (e.g., use last n diagonals) into a rigorous regression framework. The key original contribution of this paper is the discussion of how graph theory can be used to analyze the topology of an arbitrary selection of triangle cells, and how to use the information gained to set up a regression model that is suitable for projecting future development. Once properly specified, fitting a GLM using maximum likelihood estimation (MLE) is straight forward, and we describe how this can be accomplished from a practical point of view in Visual Basic. To round off our discussion of model fitting, we briefly describe the standardization of residuals, and how to plot them for graphically evaluating goodness of fit. Finally we briefly discuss how the described class of GLMs for development triangles compares to some other stochastic models proposed in the actuarial literature.

Keywords: Generalized Linear Modeling, Reserving Methods, Regression, Data Diagnostics, Data Visualization, Bootstrapping, and Resampling Methods.