Predictive Modeling Applications in Actuarial Science

Chapter 18 - Claims Triangles/Loss Reserves


Greg Taylor | University of New South Wales

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This chapter considers the application of predictive models to insurance claims triangles and the associated prediction problem of loss reserving (Section 18.1).

This is approached initially by reference to the chain ladder, a widely used heuristic reserving algorithm. Rigorous predictive models, in the form of Generalized Linear Models, that reproduce this algorithm are explored (Section 18.2).

The chain ladder has a restricted model structure and a number of embellishments are considered (Section 18.3). These include the incorporation in the model of accident year effects through the use of exposure data (e.g. accident year claim counts) (Section 18.3.2), and also the incorporation of claim closure data (Section 18.3.3).

A subsequent section considers models that incorporate claim closure data on an operational time basis (Section 18.3.4). In each of these cases emphasis is placed on the ease of inclusion of these model features in the GLM structure.

Hitherto, all models in this chapter have related to conventional claims triangles. These data sets are aggregate, as opposed to unit record claim data sets that record detail of individual claims. The chapter closes with a brief introduction to individual claim models (18.4). On occasion these use survival analysis as well as GLMs.