18 - Claims Triangles/Loss Reserves

Summary

Chapter Preview. 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 (GLMs) that reproduce this algorithm, are then 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. All models in Sections 18.1 to 18.3 relate to conventional claims triangles. These datasets are aggregate, as opposed to unit record claim datasets that record detail of individual claims. The chapter closes with a brief introduction to individual claim models (18.4). On occasion these models use survival analysis as well as GLMs.

Introduction to Loss Reserving

18.1.1 Meaning and Accounting Significance of Loss Reserving

Typically, property & casualty (P&C) insurance will indemnify the insured against events that occur within a defined period.