Link to this article: http://journals.cambridge.org/abstract_S1474747205002088How to cite this article: GEOFFREY KINGSTON and SUSAN THORP (2005). Annuitization and asset allocation with HARA utility.
AbstractA new explanation for the well-known reluctance of retirees to buy life annuities is due to 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.
This study introduces a retirement decision into the class Merton model. A familiar result is that you should retire if and when the marginal utility of another year's wages is equal to the disutility of work.A new result is that at the point of retirement your exposure to risky assets should not jump. Under power utility and constant time preference, the retirement timing problem has a closed form solution; the nine inputs to the formula in question give rise to nine comparative-static results on retirement timing. Further specialization of preference, to log consumption utility and zero time preference, reduces the required number of inputs to four. (Copyright: Elsevier)retirement, life cycle model, optimal stopping problem
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