IAI Actuarial Core Principles · Economic Modelling · Ruin theory
In a discrete-time surplus process U_n = u + cn − S_n, where S_n is the sum of n independent annual aggregate claims, which statement about the probability of ruin by time N (finite horizon) is correct?
The finite-horizon ruin probability is never larger than the infinite-horizon one, because ruin by time N is a subset of ruin at any time. It increases as the horizon lengthens and falls with higher initial surplus.
- AIt is never larger than the probability of ruin over an infinite horizonCorrect
- BIt is never smaller than the probability of ruin over an infinite horizon
- CIt is independent of the initial surplus u
- DIt decreases as the horizon N is lengthened
- It equals the probability that U_N alone is negative
Explanation
Ruin within N years is an event contained in ruin within an infinite horizon, so the finite-horizon ruin probability cannot exceed the infinite-horizon one. It rises (weakly) as N lengthens, and it depends on u. Ruin by N counts any year up to N with negative surplus, not only the final year.
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