A Fast Bipartite Algorithm for Fair Tontines

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.