Credibility Rating for a Group Health Renewal
A group health insurer must renew an employer’s policy covering 500 lives. The manual premium is ₹20,000 per life-year, built on an expected claim cost of ₹12,000 per life-year plus expenses and risk margin. The employer’s last three years of experience are: year 1 claims ₹92,00,000; year 2 ₹1,15,00,000; year 3 ₹1,28,00,000, with 500 lives exposed in each year. There was one large claim of ₹45,00,000 in year 3; the next largest claim was ₹8,00,000. The insurer uses limited fluctuation credibility with a full credibility standard of 1,082 claims at 90% confidence and ±5%, and the expected claim frequency is 0.20 claims per life-year. The underwriter wants to use the full observed claim cost because the three-year average is well above the manual rate. The actuary must compute a credibility-weighted claim cost and advise on large-claim treatment before the renewal quotation is issued.
1. Calculate the full credibility standard in exposure terms, the credibility factor, and the credibility-weighted claim cost per life-year before any large-claim adjustment.
Read the worked answer
Full credibility in exposure terms = 1,082 claims / 0.20 claims per life-year = 5,410 life-years. The employer has 500 × 3 = 1,500 life-years, so
Z = √(1,500 / 5,410) = √0.2773 = 0.5266.
Total observed claims = ₹92,00,000 + ₹1,15,00,000 + ₹1,28,00,000 = ₹3,35,00,000. Observed claim cost per life-year = ₹3,35,00,000 / 1,500 = ₹22,333.33. The manual expected claim cost is ₹12,000 per life-year. The credibility-weighted claim cost is
0.5266 × 22,333.33 + 0.4734 × 12,000 = ₹17,442 per life-year.
This is the claim-cost component only; expenses and risk margin must be added separately to get the renewal premium.
2. How does the large claim affect the result? Recommend a defensible treatment and its effect on the renewal premium.
Read the worked answer
The ₹45,00,000 claim is 13.4% of total claims and is 5.6 times the next largest claim. It is a real claim, but it is highly volatile and should not be fully credible in a three-year experience rating. Excluding it, total claims become ₹2,90,00,000 and observed claim cost becomes ₹19,333.33 per life-year. The credibility-weighted claim cost falls to
0.5266 × 19,333.33 + 0.4734 × 12,000 = ₹15,862 per life-year.
The large claim therefore adds about ₹1,580 per life-year to the indicated claim cost. A defensible treatment is to cap experience at, say, ₹8,00,000 per claim, or to apply an excess-of-loss layer, and add a separate large-claim load based on expected frequency and severity. Do not simply ignore the claim; disclose the treatment and show the renewal premium with and without the large-claim adjustment.
3. Is limited fluctuation credibility appropriate here compared with a Bühlmann or empirical Bayes approach?
Read the worked answer
Limited fluctuation credibility is transparent and easy to explain, but it uses only claim-count volume and assumes the employer is drawn from a homogeneous population. It does not use the between-employer variance and is sensitive to the large claim. A Bühlmann or empirical Bayes approach would estimate the credibility factor from the portfolio’s between-group and within-group variance, which is more appropriate when claim severity is heavy-tailed. With only 1,500 life-years and one large claim, however, the variance estimate would be unstable. A practical next step is to use limited fluctuation for the main indication, cap the large claim, and test sensitivity with a Poisson-gamma model once more years of data are available. Also check whether the employer’s industry or age mix explains part of the excess.