Triangle-free reserving vs triangle-based methods: An empirical comparison based on controlled data

Speaker(s): Alberto Glionna (Generali), Pietro Parodi (SCOR)

In Parodi (2014) it was argued that "all reserving methods based on claims triangulations, no matter how sophisticated the subsequent processing of the information contained in the triangle is, are inherently inadequate to accurately model the distribution of reserves, although they may be good enough to produce a point estimate of such reserves", and a frequency/severity approach to reserving similar to that used in pricing was proposed and called "triangle-free reserving (TFR)" in that it used the full granular information of individual historical claims to calibrate the model for the outstanding liabilities.

A rough-and-ready comparison of TFR with a standard triangle-based method (Mack's method with a lognormal distribution) was performed based on controlled data, showing the TFR method to be more accurate in assessing the aggregate loss distribution of outstanding liabilities. However, the comparison method lacked statistical rigour and was largely anecdotal.

This paper builds up on those initial tests present the results of a systematic, large-scale comparison of TFR with two classic triangle-based method, Mack's with lognormal distribution and chain ladder with bootstrap reserving using controlled data, under a variety of scenarios involving short/long-tail business, different average claim count and volatility. To make this comparison fair, a basic version of TFR with very limited modelling was used, and but not any information on how the controlled data was generated during modelling. The findings confirm the greater predictive power of TFR showing that:

1. the standard error on the best estimate for TFR is significantly lower (16%-77% of Mack/bootstrap's standard error depending on the scenario);

2. the distribution of o/s liability is closer to the real one (Kolmogorov-Smirnov distance 13%-58% of Mack's; 11%-46% of bootstrap's);

3. and this is particularly true in the tail (Anderson-Darling distance 9%-77% of Mack's; 7%-41% of bootstrap's).