IAI Actuarial Core Principles · Economic Modelling · Ruin theory
A compound Poisson surplus process has exponential claims with mean ₹50,000 and premium loading θ = 0.25. What is the probability of ultimate ruin with zero initial surplus?
The ruin probability is 0.80. With zero initial surplus, ruin probability equals 1/(1+θ), which is 1/1.25. The mean claim size of ₹50,000 does not matter, since the result holds for any claim distribution in the classical model.
- A0.25
- B0.75
- C0.80Correct
- D0.20
- 1.00
Explanation
For any claim size distribution with a finite mean in the classical model, ψ(0) = 1/(1+θ). Here 1/1.25 = 0.80. The 0.75 option wrongly uses 1−θ, and 0.20 is the survival probability 1−ψ(0), not the ruin probability.
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