Skip to content

IAI Actuarial Core Principles · Actuarial Mathematics for Modelling · Assurance and annuity functions involving two lives

For two lives (x) and (y) with independent future lifetimes, which expression correctly gives the value of a last-survivor annuity-due payable annually while at least one of them is alive?

The last-survivor annuity-due equals a_x plus a_y minus the joint-life annuity a_xy. Each payment occurs if at least one life survives, with probability tpx + tpy − tpxy, so the joint-life term is subtracted to avoid double counting.

  1. Aa_xy-due + a_x-due + a_y-due
  2. Ba_x-due + a_y-due − a_xy-dueCorrect
  3. Ca_x-due + a_y-due + a_xy-due
  4. Da_xy-due − a_x-due − a_y-due
  5. a_x-due × a_y-due / a_xy-due

Explanation

A payment is made if (x) survives or (y) survives. The probability of at least one surviving is tpx + tpy − tpx·tpy, which is tpx + tpy − tpxy. Discounting and summing gives a_x + a_y − a_xy. Adding the joint-life term would double count the case where both survive.

Did you get it right without looking?

One question tells you little. A timed set on Assurance and annuity functions involving two lives shows your real accuracy, how long you take and where you lose marks.

Practise Assurance and annuity functions involving two livesFree diagnostic mock

More Assurance and annuity functions involving two lives questions