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IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Projecting expected future cashflows and profit testing

In a unit-by-unit profit test of a life policy, the profit vector gives the expected profit at the end of each policy year per policy in force at the start of that year. How is the profit signature (profit per policy issued) derived from it?

The profit signature is found by multiplying each profit vector element by the probability that the policy is in force at the start of that year, converting profit per policy in force into profit per policy originally issued.

  1. ADivide each profit vector element by the probability that the policy is in force at the start of that year
  2. BMultiply each profit vector element by the probability that the policy is in force at the start of that yearCorrect
  3. CMultiply each element by the probability of death in that year
  4. DDiscount each element at the risk discount rate for one extra year
  5. Multiply each element by the probability that the policy is in force at the end of that year

Explanation

The profit vector is conditional on the policy being in force at the start of the year. To obtain profit per policy issued, each element is weighted by the probability of being in force at the start of that year. Weighting by the end-of-year survival probability would wrongly allow for the current year's decrement twice.

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