Recursive Credibility: Using Credibility to Blend Reserve Assumptions

By Marcus M. Yamashiro

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Abstract

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.

Keywords: Loss Reserving, Chain Ladder, Credibility

Citation

Yamashiro, Marcus M., "Recursive Credibility: Using Credibility to Blend Reserve Assumptions," Variance 8:2, 2014, pp. 105-137.

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Mission Statement

Variance (ISSN 1940-6452) is a peer-reviewed journal published by the Casualty Actuarial Society to disseminate work of interest to casualty actuaries worldwide. The focus of Variance is original practical and theoretical research in casualty actuarial science. Significant survey or similar articles are also considered for publication. Membership in the Casualty Actuarial Society is not a prerequisite for submitting papers to the journal and submissions by non-CAS members is encouraged.