IAI Actuarial Core Principles · Economic Modelling · Ruin theory
For a compound Poisson surplus process with exponential claims of mean Rs 5 lakh and relative safety loading θ = 0.25, the ruin probability is ψ(u) = (1/(1+θ)) exp(−θu/((1+θ)μ)). What is ψ(0)?
ψ(0) equals 0.80. With zero initial surplus the exponential factor is one, leaving 1/(1+θ) = 1/1.25. The result does not depend on the mean claim size.
- A0.25
- B0.50
- C0.75
- D0.80Correct
- 1.00
Explanation
At u = 0 the exponential term is 1, so ψ(0) = 1/(1+θ) = 1/1.25 = 0.80. Note this is independent of the mean claim size. 0.75 would wrongly use 1−θ.
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