An Empirical Investigation of the Value of Claim Closure Count Information to Loss Reserving
By Greg Taylor, Jing Xu
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 of the emerging numerical evidence.
The chain ladder is seen as susceptible to forecast error when applied to a portfolio characterized by material changes over time in rates of claim closure. 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 Finalized (PPCF), that rely on claim count data. The latter model in particular is intended to control for changes in claim closure rates. Each model is used to estimate loss reserve and the associated prediction error.
A compelling narrative emerges. For the selected data sets, the success of the chain ladder is limited. Either the PPCI or the PPCF model produces, or both produce, at least equal performance, in terms of prediction error, 80% of the time, and positively superior performance two-thirds 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 closure that show comparatively little variation over time.
Keywords: Bootstrap, chain ladder, count data, loss reserving, payments per claim finalized, payments per claim incurred, PPCF, PPCI, prediction error