The Extended Link Ratio Family (ELRF) and the Probabilistic Trend Family (PTF) modeling frameworks are described in the paper "Best Estimates for Reserves" (PCAS, 2000, included in CAS Syllabus of Examinations). In ELRF, average weighted link ratios (development factors) are formalized as regression estimators (Mack method), and extended to include other modeling components of interest (eg. intercepts, Murphy method). Resulting benefits include forecast standard error and testing that assumptions made by the model are supported by the data. In the PTF framework a model is built that captures the variation in the incremental loss development array, which is described using trends in the three directions: development period, accident period and calendar period and the variability of the data about the trend structure. The identified model fits (and projects for the future) lognormal distributions to each cell in the development array, conditional on certain explicit assumptions related to the historical experience, which can be amended as desired.
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