Skip to content

IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Means and variances of assurance and annuity payments

Which statement about the variance of the present value of a whole life assurance with a benefit that increases with the year of death is correct?

The variance is the second moment minus the square of the mean. The second moment uses squared benefit amounts discounted at v squared, which corresponds to force of interest 2δ, because Z squared equals b squared times v to the power 2(K+1).

  1. AIt equals the second moment of the present value minus the square of the mean, and the second moment uses discounting at force 2δ with squared benefits.Correct
  2. BIt equals the second moment, calculated at the same interest rate as the mean, minus the mean.
  3. CIt equals the mean computed at double the rate of interest.
  4. DIt is obtained by squaring the variance of the level assurance and multiplying by the highest benefit.
  5. It is zero once the benefit is deterministic at the policy outset.

Explanation

Var = E[Z²] − (E[Z])². For Z = b_{K+1} v^{K+1}, Z² = b² v^{2(K+1)}, so the second moment uses squared benefits and discount factor v², i.e. force 2δ. It is not the second moment minus the mean, and the variance is not zero because the timing of death is random.

Did you get it right without looking?

One question tells you little. A timed set on Means and variances of assurance and annuity payments shows your real accuracy, how long you take and where you lose marks.

Practise Means and variances of assurance and annuity paymentsFree diagnostic mock

More Means and variances of assurance and annuity payments questions