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IAI Actuarial Core Principles · Economic Modelling · Ruin theory

In the classical compound Poisson surplus process U(t) = u + ct − S(t), which statement about the premium loading condition is correct for ruin probability to be less than 1 for every initial surplus u > 0?

The premium rate must exceed the expected claims rate λE[X], giving a positive safety loading. Only then does the surplus drift upward on average so that ruin probability is below one. With zero or negative loading, ruin is certain eventually.

  1. APremium income rate c must exceed the expected claim outgo rate λE[X]Correct
  2. BPremium income rate c must equal λE[X]
  3. CPremium income rate c must exceed λE[X²]
  4. DPremium income rate c must be less than λE[X] so that claims are covered by capital
  5. Premium income rate c must exceed the maximum possible individual claim

Explanation

Ruin is not certain only if there is positive expected drift in the surplus, i.e. c > λE[X] (positive safety loading). If c = λE[X] the drift is zero and ruin is certain eventually; the second moment condition is irrelevant.

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