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

Non-unit cash flows (per policy in force at the start of each year, before reserves) are: time 0: -2,000; time 1: +900; time 2: +1,500. A single policy is assumed to stay in force for 2 years (no decrements). Non-unit reserves are set by zeroisation, and the insurer earns 5% p.a. on the reserves. Reserve at time 0 (after the time-0 cash flow) is V0 and at time 1 is V1; the reserve at time 2 is zero. What is V0?

The keyed option is wrong as stated; the correct reserve is Rs 2,000.

  1. ARs 0Correct
  2. BRs 1,100.00
  3. CRs 1,142.86
  4. DRs 1,428.57
  5. Rs 2,000.00

Explanation

Zeroisation at time 0 requires the cash flow plus reserve to be zero: V0 = 2,000 at time 0 (reserve needed to cover the negative cash flow). Check time 1: (V0 + CF0 where CF0 = -2,000 gives net 0) ... hence the correct reserve must make time 0 profit zero, so V0 = 2,000 only if no later reserve is released; but at time 1 cash flow is 900 + interest on 2,000 = 100, total 1,000, so the reserve V1 = 0 and V0 = 2,000.

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