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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Gross random future loss

For an in-force policy at duration t, the gross premium reserve is defined as the expected value of the gross future loss random variable. Which expression gives the gross future loss at time t, given survival to t?

The gross future loss at time t equals the present value of future benefits plus future expenses minus the present value of future gross premiums. The gross premium reserve is its expected value. It looks forward from time t and includes expenses, unlike a net premium reserve.

  1. APV of future benefits less PV of future net premiums
  2. BPV of future benefits plus PV of future expenses less PV of future gross premiumsCorrect
  3. CPV of future benefits plus PV of future gross premiums less PV of future expenses
  4. DPV of past premiums accumulated less PV of past claims and expenses
  5. PV of future gross premiums less PV of future benefits only

Explanation

The gross future loss is the present value of outgo (benefits and expenses) minus the present value of income (gross premiums), all from time t onwards. Its expectation is the gross premium reserve. Using net premiums, ignoring expenses, or reversing the sign of the premiums gives a different quantity.

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