A Fast Bipartite Algorithm for Fair Tontines

20 Pages Posted: 24 May 2011

Date Written: May 22, 2011

Abstract

In a fair tontine, members of a group contribute to a pool, and each time a member dies, his or her contribution is divided among surviving members in unequal portions according to a fair transfer plan (FTP). Constructing the FTP is a special case of the restricted transportation problem. We show that an FTP can be constructed in linear time using a greedy algorithm, even though the FTP problem does not possess the Monge property usually needed for a greedy algorithm to work. Our main result is a separable FTP, which can be constructed in linear time, and which has the desirable property that each member receives a roughly fixed proportion of a dying member's contribution.

Keywords: annuity, tontine, transportation problem, greedy algorithm, Monge, FTP, bipartite

JEL Classification: C63

Suggested Citation

Sabin, Michael J., A Fast Bipartite Algorithm for Fair Tontines (May 22, 2011). Available at SSRN: https://ssrn.com/abstract=1848737 or http://dx.doi.org/10.2139/ssrn.1848737

Michael J. Sabin (Contact Author)

Independent ( email )

Sunnyvale, CA 94087

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