Extended Link Ratio Family (ELRF)
The Extended Link Ratio Family (ELRF) modelling framework is described in the paper "Best Estimates for Reserves", published in the Proceedings of the CAS, Volume LXXXVII, 2000. The paper is also included in the 2005 Casualty Actuarial Society Syllabus of Examinations.
Both ICRFS-Plus and ICRFS-ELRF contain the ELRF modelling framework. The ELRF modelling framework is an extension of the Link Ratio Techniques (LRT module) where average weighted link ratios are formalized as regression estimators through the origin. The framework provides statistical tests of link ratio methods including Mack, Murphy, and many extensions thereof. A second example is available here.
Model assumptions are explicit and can be tested
The ELRF regression framework provides the ability to determine statistically whether the selected link ratios quantify salient features of the data and whether they have any predictive power. Additional modelling components can be added and tested. These include intercepts and constant trends for each development period across the accident periods. Forecast standard errors are easily obtained for any fitted model in the framework.
Example: Company ABC
The following residual displays are obtained for company ABC for the volume weighted average link ratio method. This array is also discussed in the paper "Best Estimates for Reserves".
It is clear from the residuals versus calendar year display (bottom left) that there is a major calendar year trend change in 84-85.
It is impossible for link ratios to capture calendar year trend changes. This is one of the reasons the PTF modelling framework was created.
ICRFS-ELRF is available free from Insureware!
See the ICRFS-ELRF training videos for a demonstration of ICRFS-ELRF functionality and use.