The Simple Analytics of a Pooled Annuity Fund

24 Pages Posted: 31 Aug 2005

See all articles by John Piggott

John Piggott

University of New South Wales (UNSW) - Australian School of Business, School of Economics

Emiliano Valdez

University of New South Wales (UNSW) - School of Actuarial Studies

Bettina Detzel

University of Karlsruhe

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.

Suggested Citation

Piggott, John and Valdez, Emiliano and Detzel, Bettina, The Simple Analytics of a Pooled Annuity Fund. Journal of Risk and Insurance, Vol. 72, No. 3, pp. 497-520, September 2005. Available at SSRN: https://ssrn.com/abstract=783000

John Piggott (Contact Author)

University of New South Wales (UNSW) - Australian School of Business, School of Economics ( email )

High Street
Sydney, NSW 2052
Australia

Emiliano Valdez

University of New South Wales (UNSW) - School of Actuarial Studies ( email )

Sydney NSW 2052, ACT 2600
Australia

Bettina Detzel

University of Karlsruhe ( email )

Postbox
D-76128 Karlsruhe, DE 76128
Germany

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