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IAI Actuarial Core Principles · Economic Modelling · Ruin theory

A company's surplus follows a compound Poisson process with adjustment coefficient R = 0.0005 per rupee. Its initial surplus is ₹6,000. By Lundberg's inequality, which is the best upper bound for the probability of ultimate ruin?

The bound is ψ(u) ≤ e^{−Ru} = e^{−0.0005×6000} = e^{−3} ≈ 0.0498, so ruin probability is at most about 5%.

  1. Ae^{-0.3}≈0.741
  2. Be^{-3}≈0.0498Correct
  3. Ce^{-6}≈0.0025
  4. De^{-30}
  5. 0.0005

Explanation

Lundberg's inequality gives ψ(u) ≤ e^{-Ru}. Here Ru = 0.0005×6,000 = 3, so the bound is e^{-3} ≈ 0.0498. The option e^{-0.3} arises from a decimal slip.

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