Pricing and Underwriting for General Insurance
Pricing questions test whether you can build a rate from evidence rather than opinion: estimate the risk cost, add the right expenses, reward the capital used, and explain the uncertainty.
Building the pure premium
- Experience (burning cost): losses ÷ exposure, after on-levelling for rate changes and trending for inflation and frequency.
- Frequency-severity: a GLM for claim counts (Poisson or negative binomial) and average cost (gamma), which copes better with thin data and lets you price individual rating factors.
- Exposure rating: used where the insurer has no credible experience - especially large or catastrophe-exposed risks.
- Credibility: weight the insured's own experience against the class rate (Bühlmann or classical credibility) so small accounts are not priced on noise.
Loading for expenses, profit and risk
Gross premium = (pure premium + per-policy fixed cost) ÷ (1 − variable expense ratio − target profit margin), plus explicit loadings for catastrophe, large-loss volatility and the cost of capital. Where a line is tariffed (regulator-notified motor third-party rates, for example), price is fixed, so margin is managed through mix, expenses and claims handling instead.
Worked example
Five years of on-levelled, trended losses total ₹4.8 crore over 40,000 vehicle-years, so pure premium = ₹4,80,00,000 ÷ 40,000 = ₹1,200. Variable expenses are 25% of premium and the target underwriting margin is 5%. Gross premium = 1,200 ÷ (1 − 0.25 − 0.05) = ₹1,714 per vehicle-year. Adding a 10% catastrophe/volatility loading before the division gives 1,320 ÷ 0.70 ≈ ₹1,886.
Traps
Forgetting on-levelling or trend; loading expenses onto the pure premium and then again onto gross; leaving one large loss in the average instead of modelling it separately; pricing to a loss-ratio target without checking that the target margin covers capital.