Best Estimates for Reserves

In recent years a number of authors (Brosius, 1992; Mack, 1993, 1994; and Murphy, 1994) have shown that link ratio techniques for loss reserving can be regarded as weighted regressions of a certain kind. We extend these regression models to handle different exposure bases and modelling of trends in the incremental data, and develop a variety of diagnostic tools for testing the assumptions these techniques carry with them. The new 'extended link ratio family' (ELRF) of regression models is used to test the assumptions made by the standard link ratio techniques and compare their predictive power with modelling (trends in) the incremental data. Not only does the ELRF of regression models indicate that for most, if not all, cumulative arrays the assumptions made by the standard link ratio techniques are not satisfied by the data, but that modelling the trends in the (log) incremental data has more predictive power. The ELRF modelling structure creates a bridge to a statistical (probabilistic) modelling framework where the assumptions are more in keeping with what we see in actual data. There is a paradigm shift from the standard link ratio techniques to the statistical modelling framework; and the ELRF can be regarded as the bridge from the 'old' paradigm to the 'new'. There are three (critical) stages involved in arriving at a reserve figure, namely, extraction of information from the data in terms of trends and stability thereof, and distributions about trends; formulation of assumptions about the future leading to forecasting of distributions of paid losses; and correlation between lines and security level sought. Finally, other benefits of the new statistical paradigm are discussed, including segmentation, credibility and reserves or distributions for different layers.