Recursive Credibility: Using Credibility to Blend Reserve Assumptions

When estimating loss reserves, actuaries usually give varying weights to multiple indications to arrive at their final selected indication. The common practice is to give weight to indications that have been developed to their ultimate expected amount. Alternatively, weight could be given to each recursive indication of paid and incurred losses, essentially averaging assumptions iteratively rather than waiting until the final estimate before selecting weights. The Munich chain ladder (MCL) is closely related to such an approach; in fact, each of the paid and incurred estimates is essentially equivalent to the recursively weighted sum of two indications, the chain ladder and a second indication, coined in this paper, the “cross link.” However, the Munich chain ladder can at times be unstable, so a different approach may be more appropriate. The framework described in this paper is a direct recursive credibility approach. By contemplating the variance of credibility weights themselves, it is an improvement in stability compared to the MCL. It also offers the possibility of recursive application of credibility to other pairs of model assumptions, and it may be generalizable to more than two pairs of assumptions.