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The Simple Analytics of a Pooled Annuity Fund

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  • John Piggott
  • Emiliano A. Valdez
  • Bettina Detzel

Abstract

This article provides a formal analysis of payout adjustments from a longevity risk-pooling fund, an arrangement we refer to as group self-annuitization (GSA). The distinguishing risk diffusion characteristic of GSAs in the family of longevity insurance instruments is that the annuitants bear their systematic risk, but the pool shares idiosyncratic risk. This obviates the need for an insurance company, although such instruments could be sold through a corporate insurer. We begin by deriving the payout adjustment for a single entry group with a single annuity factor and constant expectations. We then show that under weak requirements a unique solution to payout paths exists when multiple cohorts combine into a single pool. This relies on the harmonic mean of the ratio of realized to expected survivorship rates across cohorts. The case of evolving expectations is also analyzed. In all cases, we demonstrate that the periodic-benefit payment in a pooled annuity fund is determined based on the previous payment adjusted for any deviations in mortality and interest from expectations. GSA may have considerable appeal in countries which have adopted national defined contribution schemes and/or in which the life insurance industry is noncompetitive or poorly developed. Copyright The Journal of Risk and Insurance.

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Bibliographic Info

Article provided by The American Risk and Insurance Association in its journal The Journal of Risk and Insurance.

Volume (Year): 72 (2005)
Issue (Month): 3 ()
Pages: 497-520

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Handle: RePEc:bla:jrinsu:v:72:y:2005:i:3:p:497-520

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Cited by:
  1. Kam Ki Tang & Jie Zhang, 2007. "Morbidity, Mortality, Health Expenditures and Annuitization," CESifo Working Paper Series 2086, CESifo Group Munich.
  2. Raimond Maurer & Olivia S. Mitchell & Ralph Rogalla & Ivonne Siegelin, 2014. "Accounting and Actuarial Smoothing of Retirement Payouts in Participating Life Annuities," NBER Working Papers 20124, National Bureau of Economic Research, Inc.
  3. Vasily Kartashov & Raimond Maurer & Olivia S. Mitchell & Ralph Rogalla, 2011. "Lifecycle Portfolio Choice with Systematic Longevity Risk and Variable Investment-Linked Deferred Annuities," NBER Working Papers 17505, National Bureau of Economic Research, Inc.
  4. Catherine Donnelly, 2013. "Actuarial fairness and solidarity in pooled annuity funds," Papers 1311.5120, arXiv.org, revised Jul 2014.
  5. Hanewald, Katja & Piggott, John & Sherris, Michael, 2013. "Individual post-retirement longevity risk management under systematic mortality risk," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 87-97.
  6. Valdez, Emiliano A. & Piggott, John & Wang, Liang, 2006. "Demand and adverse selection in a pooled annuity fund," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 251-266, October.
  7. Donnelly, Catherine & Guillén, Montserrat & Nielsen, Jens Perch, 2014. "Bringing cost transparency to the life annuity market," Insurance: Mathematics and Economics, Elsevier, vol. 56(C), pages 14-27.
  8. Palmer, Edward, 2011. "Generic NDC - Equilibrium, Valuation and Risk Sharing with and without NDC Bonds," Working Paper Series 2011:3, Uppsala University, Department of Economics.
  9. Donnelly, Catherine & Guillén, Montserrat & Nielsen, Jens Perch, 2013. "Exchanging uncertain mortality for a cost," Insurance: Mathematics and Economics, Elsevier, vol. 52(1), pages 65-76.
  10. Chao Qiao & Michael Sherris, 2011. "Managing Systematic Mortality Risk with Group Self Pooling and Annuitisation Schemes," Working Papers 201104, ARC Centre of Excellence in Population Ageing Research (CEPAR), Australian School of Business, University of New South Wales.

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