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

A whole life assurance pays a sum assured S at the end of the year of death. Level premiums of P are payable annually in advance while the policyholder is alive. An initial expense of E is incurred at issue and there are no other expenses. K is the curtate future lifetime at issue and v is the annual discount factor. Which expression gives the gross random future loss at issue?

The loss is S v^{K+1} + E − P ä_{K+1}. The death benefit is paid at the end of year K+1, the initial expense is incurred at time 0, and premiums are paid in advance for K+1 years, so an annuity-due is subtracted.

  1. AS v^K + E − P ä_{K}
  2. BS v^{K+1} − E − P ä_{K+1}
  3. CS v^{K+1} + E − P ä_{K+1}Correct
  4. DS v^{K+1} + E − P a_{K+1}
  5. S v^{K} + E − P ä_{K+1}

Explanation

The benefit is paid at the end of policy year K+1, so its present value is S v^{K+1}. Premiums are paid in advance for K+1 years, giving P ä_{K+1}. The initial expense adds to the loss at time 0. Using an annuity-immediate or K in place of K+1 misstates the timing of the benefit or premiums.

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