Pricing and ratemaking for general insurance
This domain tests technical pricing: exposure bases, frequency-severity decomposition, rating factors, credibility, expenses, profit loads and the difference between technical and market prices.
Core pricing
Pure premium = expected claim frequency x expected claim severity per unit of exposure. Exposure bases include vehicle-years, payroll, turnover and sum insured. Rating factors must be statistically justified and socially acceptable. GLMs with a log link and Poisson or Tweedie error are standard; an offset handles varying exposure. Credibility blends own experience with a larger reference group; Bühlmann and limited-fluctuation credibility are common. Expenses split into fixed, variable and acquisition. The gross premium must cover pure premium, expenses, profit and risk load. Catastrophe load is added separately.
Worked example
A motor portfolio has 10,000 car-years, 800 expected claims and average severity INR 25,000. Pure premium = (800 x 25,000) / 10,000 = INR 2,000. Expenses are 20% of gross premium and target underwriting profit is 5%. Gross premium = 2,000 / (1 - 0.20 - 0.05) = INR 2,666.67. Adding 25% of pure premium would give INR 2,500, which under-recovers because expense and profit loads apply to the gross premium, not the pure premium.
Traps
Do not add percentage loads to the pure premium; divide by one minus the load. Do not use written exposure for earned risk without adjustment. Ignore mix-of-business change at your peril. GLM offsets are not optional when exposure varies. Paid loss ratios need development before use.