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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Non-unit reserves for unit-linked contracts (zeroisation)

A unit-linked policy has non-unit reserves of Rs 40 at time 1 and Rs 30 at time 2, each per policy in force at that time. During year 2 the expected non-unit cash flow at time 2 (before interest on reserves) is -Rs 10 per policy in force at time 1. Reserves earn 5% per year, and the probability of surviving from time 1 to time 2 is 0.98. The probability that a policy in force at time 0 survives to time 1 is 0.97. What is the contribution to the profit signature at time 2 per policy in force at time 0 (to two decimal places)?

The contribution is Rs 2.52. Profit per policy in force at time 1 is 40 x 1.05 - 10 - 0.98 x 30 = 2.60, and multiplying by the 0.97 survival probability to time 1 gives 2.52.

  1. ARs 2.60
  2. BRs 1.94
  3. CRs 0.60
  4. DRs 2.00
  5. Rs 2.52Correct

Explanation

Profit per policy in force at time 1 = 40 x 1.05 - 10 - 0.98 x 30 = 42 - 10 - 29.4 = 2.60. Multiply by 0.97 for survival to time 1 to get 2.522, i.e. 2.52. Rs 2.60 omits the first-year survival. Rs 2.00 and Rs 1.94 forget the survival probability on the closing reserve. Rs 0.60 omits interest on the opening reserve.

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