IAI Actuarial Core Principles · Economic Modelling · Ruin theory
For a classical surplus process, which statement about the Lundberg inequality ψ(u) ≤ e^{−Ru} is correct?
Lundberg's inequality gives an upper bound on the ultimate ruin probability, e to the power minus R times u. The bound decreases as initial surplus increases and applies generally when a positive adjustment coefficient exists, not only for exponential claims.
- AIt gives the exact ruin probability for all claim distributions
- BIt holds only for exponential claims
- CIt gives an upper bound on ruin probability that decreases as initial surplus risesCorrect
- DIt gives a lower bound on ruin probability
- It requires the premium loading to be zero
Explanation
Lundberg's inequality bounds ψ(u) above by e^{−Ru} whenever an adjustment coefficient R>0 exists. The bound falls as u rises. It is exact only in special cases such as no-overshoot situations, and it needs a positive loading.
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