A Total Credibility Approach to Pool Reserving

Motivation: Among other services in the assigned risk market, NCCI provides actuarial services for the National Workers Compensation Reinsurance Pooling Mechanism (NWCRP), the Massachusetts Workers’ Compensation Assigned Risk Pool, the Michigan Workers’ Compensation Placement Facility, and the New Mexico Workers’ Compensation Assigned Risk Pool. Pool reserving triangles pose specific challenges as they may be sparsely populated; this is because states may have left the NWCRP, recently joined it, or re-joined it after several years of absence. Furthermore, triangles of partial coverage states may have unpopulated cells due to not having experienced a claim in a given policy year.

Method: There are two credibility aspects to Pool reserving to be addressed. First, the degree of variability of the link ratios may differ across states, possibly (but not necessarily entirely) due to differences in size of the assigned risk market across states. Second, the number of link ratios available varies greatly across states, from fully populated diagonals to very few observations per diagonal or, for some partial coverage states, to no observations at all. To address these challenges, a comprehensive credibility approach has been developed, where the credibility- adjustment applies to the data-generating process as opposed to the outcome. This new concept, called Total Credibility, rests on multilevel (hierarchical) modeling, which implies that the Pool triangles of all states are estimated simultaneously.

Results: The model is applied to the logarithmic paid plus case link ratios of the latest five diagonals of the Pool triangles of 45 jurisdictions, some of which are partial coverage states. Diagnostic charts of in-sample fit show that the model is well suited for replicating the observed data. Further, diagnostic charts of forecast errors indicate that the structure of the model is a proper representation of the data-generating process.

Availability: The model was implemented in R (http://cran.r-project.org/) using the sampling platform JAGS (Just Another Gibbs Sampler, http://www-ice.iarc.fr/~martyn/software/jags/). JAGS was linked to R by means of the R package rjags (http://cran.r-project.org/web/packages/rjags/index.html).

Keywords: Pool Reserving, Growth Curve, Total Credibility