IAI Actuarial Core Principles · Economic Modelling · Role of insurance in reducing or removing risk
An Indian insurer pools 400 independent motor policies. Each has an annual claim with mean ₹5,000 and standard deviation ₹10,000. Using a normal approximation for the total claim, what is the premium per policy that gives a 97.5% probability (z = 1.96) that total claims do not exceed premium income?
The premium is ₹5,980 per policy. The average claim has standard deviation 10,000 divided by the square root of 400, which is ₹500. Adding 1.96 times this to the mean of ₹5,000 gives the premium that covers claims with 97.5% probability.
- A₹5,980Correct
- B₹5,490
- C₹6,960
- D₹5,049
- ₹5,098
Explanation
Standard deviation of the average = 10,000/√400 = 500. Premium = 5,000 + 1.96 × 500 = 5,980. Using the total's standard deviation of 200,000 divided by 400 gives the same. ₹6,960 wrongly uses a standard deviation of 1,000 (a mistake with the root). ₹5,490 uses 0.98 × 500.
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