The Analysis of "All-Prior" Data

Motivation. Some data sources, such as the NAIC Annual Statement Schedule P as an example, contain a row of all-prior data within the triangle. While the CAS literature has a wealth of papers that have developed various methods for estimating tail factors, and the CAS Tail Factor Working Party recently published a report on tail factor methods, tail factors are not directly applicable to all-prior data. Moreover, the author is not aware of any papers dealing directly with the analysis of all-prior data. Absent a defined methodology, it seems to be common practice for an analysis of data triangles that include an all-prior row to either exclude the all-prior data or to make the explicit assumption that the case reserves, or case plus IBNR reserves, for these claims are adequate. This may be reasonable in certain situations but given the potential materiality of this part of the reserve it would be a useful addition to the actuary’s toolkit to develop some methods for analyzing the all-prior data or for testing the reasonability of assuming the case reserves, or case plus IBNR reserves, are adequate.

Method. The process followed in this paper is to both graphically and formulaically illustrate the data issues and analysis, then apply the concepts of a well-known method with three different data sets. While only a deterministic point estimate method is illustrated in this paper, the framework should be quite easily adaptable to other deterministic methods or stochastic models. The paper also illustrates the calculations for this method and examples in a companion Excel spreadsheet.

Conclusions. The methods used for any standard analysis can be adapted to accommodate all-prior data whenever it is present. Even in cases where the all-prior reserves prove adequate, the process of analyzing the all-prior data will help calibrate the tail factor used for all years by validating the selected tail factor using actual data.

Availability. The Excel spreadsheets created for this paper “All Prior Analysis.xlsm” and “Creating All Prior Data.xls” are available at http://www.casact.org/pubs/forum/14forum/.

Keywords. Reserving (Reserving Methods); Reserving (Data Organization); Reserving (Reserve Variability); Reserving (Tail Factors)