Annuitization and asset allocation with HARA utility

A new explanation for the well-known reluctance of retirees to buy life annuities is due toMilevsky and Young (2002, 2003): Since the decision to purchase longevity insurance is largelyirreversible, in uncertain environments a real option to delay annuitization (RODA) generallyhas value. Milevsky and Young analytically identify and numerically estimate the RODA in asetting 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 dateof annuitization can no longer be ascertained with certainty in advance. This paper derives anapproximation whereby the agent precommits. The effect of increasing the subsistence consumptionrate on the timing of annuity purchase is similar to the effect of increasing thecurvature parameter of the utility function. As in the CRRA case studied by Milevsky andYoung, delayed annuitization is associated with optimistic predictions of the Sharpe ratio anddivergence between annuity purchaser and provider predictions of mortality.