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Lifetime consumption and investment with housing, deferred annuities and home equity release

Jang, C., Owadally, I. ORCID: 0000-0002-0830-3554, Clare, A. ORCID: 0000-0002-4180-6778 & Kashif, M. (2021). Lifetime consumption and investment with housing, deferred annuities and home equity release. Quantitative Finance, 22(1), pp. 129-145. doi: 10.1080/14697688.2021.1993624


We develop a life-cycle optimal investment and consumption model with deferred annuities, housing, mortgages and home equity release. The investor can hold cash, bonds, stocks, annuities and can invest in housing, through renting, purchasing, or a mix of both, with access to variable-rate mortgages. In retirement, the investor can access his housing equity through a form of home equity release called a home reversion contract. Transaction costs, taxes and management fees are explicitly included. The investor’s risk preferences are represented by standard power utility derived from housing and nonhousing consumption, both before and after retirement, and from bequest. We use multi-stage stochastic programming to solve the optimization problem numerically. Our results show that both non-housing and housing consumption may be higher in retirement when deferred annuities and home reversion are available than when they are absent. The bequest motive has little effect on home reversion and results in a small reduction in overall annuitization.

Publication Type: Article
Additional Information: © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (, which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. This article has been published in Quantitative Finance, doi:
Publisher Keywords: Stochastic programming; Retirement planning; Home equity reversion; Deferred annuities
Subjects: H Social Sciences > HG Finance
Departments: Bayes Business School > Finance
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