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IAI Actuarial Core Principles · Economic Modelling · Ruin theory

Why does simulating ruin over a finite horizon by checking the surplus only at year ends in a model where claims occur continuously through the year tend to bias the estimate?

Checking only at year ends understates ruin, because the surplus could fall below zero between checks and recover before the next observation. Those short-lived ruin events are missed, so the simulated ruin probability is biased downward.

  1. AIt overstates ruin because premiums are ignored between checks
  2. BIt understates ruin because surplus may dip below zero between checks and recoverCorrect
  3. CIt has no bias because claims are independent
  4. DIt overstates ruin because the simulated claims are too large
  5. It understates ruin only when the initial surplus is zero

Explanation

Ruin is defined on the continuous path, but checking only at the discrete dates misses any dip below zero that is repaired before the next check. Hence the estimated probability is biased downwards. Independence of claims does not remove this monitoring error.

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