Abstract:
A new explanation for the well-known reluctance of retirees to buy life annuities is due to
Milevsky and Young (2002, 2003): Since the decision to purchase longevity insurance is largely
irreversible, in uncertain environments a real option to delay annuitization (RODA) generally
has value. Milevsky and Young analytically identify and numerically estimate the RODA in a
setting of constant relative risk aversion. This paper presents an extension to the case of HARA
(or GLUM) preferences, the simplest representation of a consumption habit. The precise date
of annuitization can no longer be ascertained with certainty in advance. This paper derives an
approximation whereby the agent precommits. The effect of increasing the subsistence consumption
rate on the timing of annuity purchase is similar to the effect of increasing the
curvature parameter of the utility function. As in the CRRA case studied by Milevsky and
Young, delayed annuitization is associated with optimistic predictions of the Sharpe ratio and
divergence between annuity purchaser and provider predictions of mortality.
