Optimal allocation to deferred income annuities

TL;DR

This paper develops a mathematical framework to determine optimal purchase policies for deferred income annuities using a lifecycle model that incorporates utility of consumption and bequest, analyzing how asset allocation impacts these decisions.

Contribution

It introduces a comprehensive optimization model for DIA purchase decisions, extending it to include asset allocation choices and analyzing their effects on optimal policies.

Findings

Refundable DIAs are less attractive than non-refundable DIAs due to mortality credits.

The DIA allocation region is larger under fixed asset allocation strategies.

Allowing asset allocation changes reduces the appeal of DIA investments.

Abstract

In this paper we employ a lifecycle model that uses utility of consumption and bequest to determine an optimal Deferred Income Annuity (DIA) purchase policy. We lay out a mathematical framework to formalize the optimization process. The method and implementation of the optimization is explained, and the results are then analyzed. We extend our model to control for asset allocation and show how the purchase policy changes when one is allowed to vary asset allocation. Our results indicate that (i.) refundable DIAs are less appealing than non-refundable DIAs because of the loss of mortality credits; (ii.) the DIA allocation region is larger under the fixed asset allocation strategy due to it becoming a proxy for fixed-income allocation; and (iii.) when the investor is allowed to change asset-allocation, DIA allocation becomes less appealing. However, a case for higher DIA allocation can be made for those individuals who perceive their longevity to be higher than the population.