Credibility Pricing for a Large Group Personal Accident Renewal
An Iranian non-life insurer is pricing a group personal accident (GPA) cover for a 200-employee logistics company. The manual premium is IRR 12,000 million, built on a 55% target loss ratio. The insurer has two years of experience for this employer: 400 employee-years of exposure and IRR 1,050 million of paid and reserved claims, implying an observed loss ratio of 70%. The pricing actuary uses a Bühlmann-Straub credibility model. Company standards set the credibility factor at Z = 0.45 for this amount of experience; the complement is the manual loss ratio. The employer has recently added 60 drivers and changed its safety program, and the underwriter wants a 10% discretionary discount to win the renewal. The reserving actuary has separately warned that the two-year claims figure may be understated because several late-reported claims are still in IBNR.
1. Calculate the credibility-weighted loss ratio and the indicated manual premium before any discretionary discount. Show formulas and state whether the 10% discount is supported by the indicated rate.
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Credibility-weighted loss ratio:
LR_cred = Z × LR_observed + (1 − Z) × LR_manual = 0.45 × 70% + 0.55 × 55% = 31.5% + 30.25% = 61.75%.
If expenses and the target loss ratio are unchanged, the indicated premium is the manual premium scaled by the ratio of credible to target loss ratio:
P_ind = 12,000 × (61.75 / 55) = 12,000 × 1.1227 = IRR 13,473 million approximately.
Because the indicated premium is above the manual premium, the 10% discretionary discount is not supported by the credible experience. A 10% discount would price at 10,800m, implying a loss ratio of 61.75/0.90 = 68.6% if losses stayed at the credible level, above the 55% target. The actuary should not sign the discount as actuarially justified without other evidence, such as a demonstrable expense saving or a separately justified large-loss cap.
2. The underwriter argues that because the employer is large, the observed 70% should be blended only lightly and a 10% discount granted to reflect expense savings. Evaluate this argument, including the effect of the recent fleet expansion and IBNR warning.
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Large exposure helps credibility but does not create full credibility automatically. Credibility depends on the variance of claim results, not only payroll or employee count. Here there are only two years, 400 employee-years, a recent change in exposure (60 new drivers) and a warning that late-reported claims may be missing. The observed 70% is therefore not a clean estimate of the future loss ratio.
If one or a few large claims dominate the 1,050m, the actuary should separate large losses and apply a large-loss loading or an excess-of-loss treatment, rather than either using 70% directly or ignoring it. If the IBNR is understated, the true observed loss ratio is higher than 70%, which makes a discount even less defensible. Conversely, a demonstrated expense saving from direct distribution could justify a lower expense loading, but that must be shown separately and not disguised as credibility.
3. Recommend the renewal action, including what data checks and monitoring you would require before signing the pricing note.
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Recommended renewal action:
- Do not grant the 10% discount. Price at the indicated 13,473m or hold 12,000m only with a documented plan to recover the deficiency, e.g., a safety-programme discount tied to verifiable telematics.
- Before signing, reconcile the claims extract to the claims system, estimate the missing late-reported claims, and split the experience into frequency and severity. Test sensitivity to one large claim.
- Recalculate exposure for the 60 new drivers; if they are young or long-distance, the loss ratio may rise.
- Set monitoring triggers: quarterly loss ratio above 65%, claim frequency above 12 per 100 employee-years, or two claims above 200m trigger repricing.
- If the underwriter still wants a strategic discount, require board approval, a profit test showing the account remains above the risk-adjusted hurdle, and disclosure that the discount is not actuarially indicated. Document the decision and the actuary's advice.