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IAI Actuarial Core Principles · Economic Modelling · Ruin theory

In a discrete-time surplus process, U_n = U_{n-1} + c - S_n, where c is the premium per period and S_n the aggregate claims in period n. Which statement correctly describes the probability of ruin within a finite horizon, ψ(u, N)?

Finite-horizon ruin probability is the chance that the surplus becomes negative at least once at the monitored times up to N. It is not just the chance of being negative at time N, because a path can go below zero and later recover.

  1. AIt is the probability that U_n < 0 for at least one n in 1, 2, ..., NCorrect
  2. BIt is the probability that U_N < 0 at the final time N only
  3. CIt is the probability that total premiums fall below total claims at every time n up to N
  4. DIt is the expected number of times the surplus falls below zero up to time N
  5. It is the probability that the surplus is zero at some time up to N

Explanation

Finite-time ruin means the surplus is negative at one or more of the monitored times n = 1,...,N. Option 2 looks only at the end point and so understates ruin, because surplus may recover after dipping below zero. The other options describe different quantities.

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