IAI Actuarial Core Principles · Economic Modelling · Ruin theory
A general insurer's claims follow a compound Poisson process with Poisson rate λ = 10 per year and mean claim size Rs 2 lakh. Premiums are received continuously at a rate set with a relative safety loading θ = 25%. What is the annual premium income rate c?
The premium rate is Rs 25 lakh per year. Expected annual claims are 10 × Rs 2 lakh = Rs 20 lakh, and a 25% relative safety loading multiplies this by 1.25, giving Rs 25 lakh.
- ARs 20 lakh
- BRs 22.5 lakh
- CRs 25 lakhCorrect
- DRs 27.5 lakh
- Rs 30 lakh
Explanation
Expected claims per year = 10 × 2 = Rs 20 lakh. Premium c = (1+θ)λE[X] = 1.25 × 20 = Rs 25 lakh. Rs 22.5 lakh would arise from a 12.5% loading, and Rs 20 lakh has no loading.
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