Optimal life insurance and annuity demand under hyperbolic discounting when bequests are luxury goods

Jinhui Zhang*, Sachi Purcal, Jiaqin Wei

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)
98 Downloads (Pure)


We operationalise the theoretical modelling of Marín-Solano and Jorge Navas (2010), seeking to understand the consequences for optimal consumption, life insurance and annuity demand in a time inconsistent world, by incorporating the insurance insights from Richard (1975). Richar, in particular, has an elegant treatment of optimal annuity demand, rarely harnessed in the literature. Central to Richard's creation of demand for personal insurance is a bequest motive and, in addition to implementing time inconsistency through hyperbolic discounting, our analysis is further expanded to include naïve and sophisticated agents with a luxury bequest motive (Lockwood, 2012). Compared to a more simplistic ‘necessity’ bequest framework, luxury bequests (broadly) weaken optimal life insurance demand and strengthen optimal life annuity demand for the less wealthy. In contrast, time inconsistency offers a wide spectrum of outcomes, and our modelling, calibrated to Swiss data, contributes to understanding the annuity puzzle—observed low levels of (voluntary) purchases of life annuities.

Original languageEnglish
Pages (from-to)80-90
Number of pages11
JournalInsurance: Mathematics and Economics
Volume101, Part A
Early online date6 Jul 2020
Publication statusPublished - Nov 2021

Bibliographical note

Copyright © 2020 Elsevier B.V. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.


  • Annuity puzzle
  • Dynamic programming
  • Finance
  • Hyperbolic discounting
  • Luxury bequests


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