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Life Insurance and Annuity Demand under Hyperbolic Discounting

1, 2,† and 2,*,†
The QSuper Group, 70 Eagle Street, Brisbane, QLD 4000, Australia
Department of Actuarial Studies and Business Analytics, Faculty of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Risks 2018, 6(2), 43;
Received: 29 March 2018 / Revised: 12 April 2018 / Accepted: 17 April 2018 / Published: 23 April 2018
(This article belongs to the Special Issue Optimal Demands for Life Insurance and Annuities)
PDF [1809 KB, uploaded 3 May 2018]


In this paper, we analyse and construct a lifetime utility maximisation model with hyperbolic discounting. Within the model, a number of assumptions are made: complete markets, actuarially fair life insurance/annuity is available, and investors have time-dependent preferences. Time dependent preferences are in contrast to the usual case of constant preferences (exponential discounting). We find: (1) investors (realistically) demand more life insurance after retirement (in contrast to the standard model, which showed strong demand for life annuities), and annuities are rarely purchased; (2) optimal consumption paths exhibit a humped shape (which is usually only found in incomplete markets under the assumptions of the standard model). View Full-Text
Keywords: hyperbolic discounting; dynamic programming; consumption; portfolio rules; life insurance; life annuity hyperbolic discounting; dynamic programming; consumption; portfolio rules; life insurance; life annuity

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Tang, S.; Purcal, S.; Zhang, J. Life Insurance and Annuity Demand under Hyperbolic Discounting. Risks 2018, 6, 43.

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