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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Gross premiums and reserves

A life insurer prices a policy by the equivalence principle on a stated basis covering mortality, interest and expenses, including initial expenses. It then values the policy at outset on exactly the same basis, just before the first premium is paid and initial expenses are incurred. What is the gross premium reserve at that point?

The reserve is zero. The equivalence principle sets the gross premium so that the PV of future benefits and expenses equals the PV of future gross premiums at outset. A valuation on the same basis at that moment therefore gives no liability.

  1. AEqual to the initial expense
  2. BEqual to the present value of future benefits
  3. CZeroCorrect
  4. DEqual to the net premium reserve at outset
  5. Equal to minus the initial commission

Explanation

The gross premium reserve is the PV of future benefits plus expenses minus the PV of future gross premiums. The equivalence principle sets the premium so that these two present values are equal at outset on the pricing basis. The reserve is therefore zero. The other options confuse it with the initial expense or with a net premium reserve, which is on a different basis.

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