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Optimal Purchasing of Deferred Income Annuities When Payout Yields are Mean-Reverting

37 Pages Posted: 20 Mar 2015  

Huang Huaxiong

York University

Moshe A. Milevsky

York University - Schulich School of Business

V.R. Young

University of Michigan at Ann Arbor - Department of Mathematics

Date Written: March 18, 2015

Abstract

We determine the optimal lifecycle purchasing strategy for deferred income annuities (DIAs), which are distinct from single-premium income annuities (SPIAs) for an individual who wishes to maximize the expected utility of her annuity income at a fixed time in the future. In contrast to the portfolio-choice literature for SPIAs, we focus on the "stochasticity" of the DIA's payout yield and address concerns that payout yields are currently too low to justify irreversible annuitization. After formulating and solving the optimal control problem analytically, our main qualitative result is that when payout yields are mean-reverting, a risk-neutral consumer who wishes to maximize her expected retirement income should wait until yields reach a threshold - which lies above historical averages - and, then purchase the DIA in one lump sum. In contrast, a risk-averse consumer who is concerned the payout yield will remain below average for an extended period and worries about losing mortality credits while waiting, should employ a barrier purchasing strategy, as in the portfolio choice problem under transaction costs. In fact, the optimal behavior of a risk-averse consumer resembles an asymmetric dollar-cost averaging strategy, with a portion of the DIA-budget spent even while payout rates are below historical averages. We conclude with numerical examples calibrated to a time series of DIA prices and provide some estimates of the expected purchasing time.

Keywords: deferred income annuities, stochastic interest rates, optimal stopping, instantaneous control, retirement, pensions

JEL Classification: D14, G11, G22, J26

Suggested Citation

Huaxiong, Huang and Milevsky, Moshe A. and Young, V.R., Optimal Purchasing of Deferred Income Annuities When Payout Yields are Mean-Reverting (March 18, 2015). Available at SSRN: https://ssrn.com/abstract=2580420 or http://dx.doi.org/10.2139/ssrn.2580420

Huang Huaxiong

York University ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

Moshe Arye Milevsky (Contact Author)

York University - Schulich School of Business ( email )

4700 Keele Street
Toronto, Ontario M3J 1P3
Canada

Virginia R. Young

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States
734-764-7227 (Phone)

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