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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Valuing cashflows contingent on multiple transition events

For a policy paying Rs 60,000 immediately on death, with continuous premiums of Rs 1,500 per year, the policy value at time 10 is Rs 20,000. At that time δ = 0.05 and μ = 0.01. Using Thiele's equation and one Euler step of size 1 year backwards, V(9) ≈ V(10) − 1×dV/dt at t = 10. What is the approximate policy value at time 9 (Rs)?

The approximate policy value at time 9 is Rs 17,900. The derivative at time 10 is 1,000 + 1,500 − 400 = 2,100 per year, and stepping back one year subtracts this from the value of 20,000.

  1. A18,100
  2. B17,900Correct
  3. C22,100
  4. D18,900
  5. 17,100

Explanation

dV/dt = 0.05×20,000 + 1,500 − 0.01×(60,000 − 20,000) = 1,000 + 1,500 − 400 = 2,100. Backward step: V(9) ≈ 20,000 − 2,100 = 17,900. Rs 22,100 results from stepping forward instead; Rs 18,100 results from using μS = 600 instead of μ(S − V).

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