A coherent approach to annuitisation

Which of the following two financial instruments would you prefer if you were a 65-year old (or her fi nancial advisor, or insurance company):

(A) A regular risk-free bond with a current value of 100.000 EUR;
(B) An annuity which pays off nothing in the very unlikely case (say with probability of 1%) that you die this year; whose discounted pay-off s represent 100.000 EUR if you die between now and twenty years (89%); and if you happen to live longer the equivalent of a present value of 500.000 EUR?

Secondly, would you prefer

(C) An insurance policy which pays 100.000 EUR either in the very unlikely case that you die in the next year or in the rather unlikely event you live beyond 85, and nothing otherwise;
(D) A longevity annuity which pays off the equivalent of 500.000 EUR but only if you live beyond 85, and nothing otherwise?

The reader will, of course, have recognised the paradox of Allais (1953); the Allais choice A&D contradicts expected utility theory because if you prefer A to B , U(100) > 0, 1U(500) + 0,89U(100)  which is equivalent to 0,11U(100) > 0,1U(500) , and thus you should prefer C to D and vice versa. The paradox remarkably well captures consumer behaviour in retirement planning: people are averse to immediate-start annuities but take to the lotteryticket-like longevity annuity. → Read More