An Empirical Investigation of the Value of Finalisation Count Information to Loss Reserving

Abstract

The purpose of the present paper has been to test whether loss reserving models that rely on claim count data can produce better forecasts than the chain ladder model (which does not rely on counts); better in the sense of being subject to a lesser prediction error. The question at issue has been tested empirically by reference to the Meyers-Shi data set. Conclusions are drawn on the basis the emerging numerical evidence. The chain ladder is seen as susceptible to forecast error when applied to a portfolio characterised by material changes over time in rates of claim finalisation. For this reason, emphasis has been placed here on the selection of such portfolios for testing. The chain ladder model is applied to a number of portfolios, and so are two other models, the Payments Per Claim Incurred (PPCI) and Payments Per Claim Finalised (PPCF), that rely on claim count data. The latter model in particular is intended to control for changes in finalisation rates. Each model is used to estimate loss reserve and the associated prediction error. A compelling narrative emerges. The chain ladder rarely performs well. Either PPCI or PPCF model produces, or both produce, superior performance, in terms of prediction error, 80% of the time. When the chain ladder produces the best performance of the three models, this appears to be accounted for by either erratic count data or rates of claim finalisation that show comparatively little variation over time.