IAI Actuarial Core Principles · Economic Modelling · Ruin theory
An insurer has adjustment coefficient R = 0.02 per ₹ lakh. Using Lundberg's inequality, which initial surplus u (in ₹ lakh) guarantees that the ruin probability is at most 1%? Take ln 100 = 4.605.
Set e^{-0.02u} ≤ 0.01, so 0.02u ≥ ln 100 = 4.605 and u ≥ 230.25 lakh. Lundberg's bound then guarantees ruin probability of at most one percent.
- Au ≥ 46.05
- Bu ≥ 92.1
- Cu ≥ 230.25Correct
- Du ≥ 23.03
- u ≥ 100
Explanation
We need e^{-0.02u} ≤ 0.01, so 0.02u ≥ ln 100 = 4.605, giving u ≥ 4.605/0.02 = 230.25. Option 1 divides by 0.1 and option 4 by 0.2, both errors. Option 2 multiplies by 0.02 incorrectly.
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