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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 cash flows (before reserves, per policy in force at the start of the year, at year end) of CF2 = -50, CF3 = +80 and CF4 = -60, with a reserve of zero at time 4. The survival probability is 0.99 each year and reserves earn 10% a year. Reserves are set by zeroisation and may not be negative. What is the reserve required at time 1 per policy in force at that time?

The reserve at time 1 is 45.45. The year 3 surplus of 80 more than covers the cost of the reserve needed for year 4, so V2 is zero, not negative. Only the year 2 strain of 50 remains, giving V1 = 50/1.1 = 45.45.

  1. A24.18
  2. B45.00
  3. C45.45Correct
  4. D54.55
  5. 89.63

Explanation

V3 = 60/1.1 = 54.545. Year 3: V2(1.1) + 80 - 0.99 x 54.545 = V2(1.1) + 26 >= 0, so V2 = 0 because the positive cash flow covers the later strain. Year 2: V1(1.1) - 50 = 0, so V1 = 45.45. Netting all flows without the zero floor gives 24.18, which is wrong because reserves cannot be negative.

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