Credibility and a Large Claim in Group Life Rating
An insurer is setting group life premium rates for 15 employer schemes. For each scheme it has three years of death claim amounts and employee-year exposure. Scheme A has 2,400 employee-years and an observed claim rate of 0.0042 deaths per employee-year; the portfolio average is 0.0030. Scheme B has only 180 employee-years and an observed rate of 0.0055. The actuarial team computed Bühlmann–Straub credibility factors and reports Z_A = 0.91 and Z_B = 0.42. Scheme B’s experience includes one death claim of £250,000, which is large relative to its £1.1m annual payroll. The sales team wants to apply full experience rating to Scheme B because it has a poor claims record; the underwriter worries that the single large claim is driving the result.
1. Using Z_B = 0.42, compute the credibility premium for Scheme B and compare with full experience rating. What does the difference imply?
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With Z_B = 0.42, the Bühlmann–Straub credibility premium per employee-year is Z_B × observed rate + (1 − Z_B) × portfolio mean = 0.42 × 0.0055 + 0.58 × 0.0030 = 0.00231 + 0.00174 = 0.00405. Full experience rating would charge 0.0055, about 36% more. The credibility premium is lower because 180 employee-years is limited exposure: much of the observed excess over 0.0030 could be random fluctuation, especially with only a small number of deaths. The difference is the value of pooling. This does not mean the scheme should be subsidised indefinitely; it means the data are not yet sufficient to justify full experience rating. The credibility factor also gives a natural range: the true rate is likely between the portfolio mean and the observed rate, with more weight on the observed rate as exposure accumulates.
2. The sales team wants full experience rating for Scheme B. Discuss the statistical and commercial arguments, including the single large claim.
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Statistically, full experience rating for Scheme B is not defensible. The credibility factor of 0.42 already reflects the low exposure and high process variance; using 100% weight on 180 employee-years ignores sampling error and will produce volatile, unfair premiums. A single £250,000 claim on a £1.1m payroll can dominate the observed rate. The underwriter is right to be concerned: one large claim is not evidence of a persistently bad scheme. Commercially, the sales team may want to reflect the poor record to avoid anti-selection, but over-reacting risks losing the scheme or creating a validity challenge. I would recommend: (i) use the credibility premium as the starting point; (ii) treat the large claim through a large-claim pooling arrangement or cap, rather than excluding it silently; (iii) if the claim is excluded for rating, add an explicit large-claim load and disclose it; and (iv) monitor the scheme and increase credibility as exposure grows. If the scheme has genuinely worse underlying risk, that should show up in several years of experience, not one claim.