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

A two-year unit-linked policy has non-unit cashflows (per policy, no decrements) of +Rs 30 at the end of year 1 and -Rs 121 at the end of year 2. The interest rate is 10% p.a. Using zeroisation, what is the non-unit reserve at time 0, assuming it is not negative?

The time-0 reserve is Rs 72.73. First find the year-1 reserve of Rs 110 to fund the Rs 121 outgo. Then the time-0 reserve plus the interest-bearing Rs 30 inflow must reach Rs 110, giving 80 divided by 1.1.

  1. ARs 110.00
  2. BRs 127.27
  3. CRs 80.00
  4. DRs 72.73Correct
  5. Rs 0.00

Explanation

Working backwards, V1 = 121/1.1 = 110. At time 0, V0 x 1.1 + 30 = 110, so V0 = 80/1.1 = 72.73. Rs 127.27 wrongly adds the year-1 cashflow, giving (110+30)/1.1.

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