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IAI Actuarial Core Principles · Economic Modelling · Ruin theory

Which statement about the Lundberg inequality ψ(u) ≤ e^{-Ru} in the classical compound Poisson model is correct?

Lundberg's inequality gives an upper bound, ψ(u) ≤ e^{-Ru}, valid for any claim distribution for which the adjustment coefficient R exists and the loading is positive. It is not exact in general and not a lower bound.

  1. AIt holds only for exponential claims
  2. BIt gives an exact value of ψ(u) for all claim distributions
  3. CIt requires the loading θ to be negative
  4. DIt provides an upper bound on ruin probability for any claim distribution where R existsCorrect
  5. It gives a lower bound on ruin probability

Explanation

Lundberg's inequality is an upper bound valid whenever an adjustment coefficient R exists, with positive loading. It is exact only in special cases, such as when ψ(u) = ψ(0)e^{-Ru}. A negative loading would make ruin certain.

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