IAI Actuarial Core Principles · Economic Modelling · Ruin theory
Annual aggregate claims are i.i.d. with mean Rs 90 lakh and standard deviation Rs 30 lakh. Annual premium is Rs 100 lakh, initial surplus Rs 20 lakh. Using a normal approximation for the surplus at the end of year 4 only, what is P(U_4 < 0)? (Φ(1.0)=0.8413, Φ(1.5)=0.9332, Φ(2.0)=0.9772, Φ(2.5)=0.9938)
The mean surplus at year 4 is 20 + 400 − 360 = 60 lakh, and the standard deviation is 30×2 = 60 lakh. So P(U_4<0) = Φ(−1) = 0.1587.
- A0.0668
- B0.1587Correct
- C0.0228
- D0.0062
- 0.8413
Explanation
E[U_4]=20+400−360=60. Variance of S_4 = 4×900, so SD = 60. P(U_4<0)=Φ(−60/60)=Φ(−1)=1−0.8413=0.1587. Using SD 30 would give 0.0228, forgetting the √n scaling.
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