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

A whole life policy is issued to a life aged x. It pays a sum assured S at the end of the year of death. Premiums of P are payable annually in advance for life, and an initial expense E is incurred at issue. Let K be the curtate future lifetime. Which expression gives the gross future loss random variable at issue?

The loss equals the present value of the benefit plus the initial expense, minus the present value of premiums. That is S v^(K+1) + E − P ä(K+1), because the benefit is paid at the end of the year of death and premiums are paid in advance for K+1 years.

  1. AS v^(K+1) + E − P ä(K+1)Correct
  2. BS v^K + E − P ä(K)
  3. CS v^(K+1) − E − P ä(K+1)
  4. DS v^(K+1) + E − P a(K+1)
  5. P ä(K+1) − S v^(K+1) − E

Explanation

The gross future loss is the present value of outgo (benefit plus expense) minus the present value of premium income. The benefit is paid at time K+1, and premiums are paid in advance for K+1 years, so the premium annuity is ä(K+1). Option B uses the wrong benefit and premium terms. Option E reverses the sign of the loss.

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