The fair transfer plan
What makes the sharing fair?
People bring different balances and different mortality risks. The allocation rule has to account for both.
Sharing equally would be simple, but members have different amounts at stake. A larger committed balance means more value enters the pool on death. A higher probability of death also raises the expected value being committed.
Compare the expected values
A fair transfer plan, or FTP, balances those commitments against the allocations members expect to receive. Under the mortality model, each member’s expected incoming allocations equal the expected committed balance they give up.
That equality is assessed before the event, across the possible outcomes. Once an event occurs, the available balance is allocated to the eligible survivors. The formula determines their shares, which then enter their own remaining investment ladders.
The member’s investment results remain attributable to their investments. FTP governs the sharing of committed balances between accounts.
Calculate the transfer, then check it
Michael Sabin’s fair transfer plan provides a survivor-weight rule for heterogeneous pools. This work began with a question about its interpretation: could the rule be reached by starting with a simpler allocation and finding the closest one that satisfies all the fairness conditions?
The resulting formulation puts the fairness and conservation conditions into a form that can be examined separately from the calculation proposing the transfers. One procedure finds an allocation. Another checks that the available balance is fully assigned and that each member’s expected-value condition is met.
The same approach can treat a set of deaths settled together. It tests whether fair allocations exist for that event model and gives a way to calculate them. The first methods note defines the starting allocation—called nominal gain—and sets out the interpretation and conditions.
A calculation with a separate check
- 01Declare the inputs
Balances, mortality assumptions and eligible recipients.
- 02Propose allocations
Find transfers that satisfy the stated fairness conditions.
- 03Check independently
Reconcile every balance and each member’s expected value.
- 04Settle and record
Issue instructions only after the required checks pass.
Account for the pool that remains
An allocation changes the surviving members’ balances. As the pool becomes smaller, one member or group may represent too much of the mortality-weighted exposure for the next allocation to be fair.
The continuation research adds that next requirement to the current calculation. Some examples can be repaired by choosing another allocation that is fair today and leaves the required successor pools feasible. Other examples contain a mathematical conflict between those requirements.
The research includes specified next batches of two or three deaths. The capacity examples explain what changes and why a transfer to another pool is being considered.
Turn the rule into an operating policy
Admissions, investment changes and scheduled releases all alter the remaining accounts. A pension therefore needs rules for when the checks run and what happens if the pool can no longer support its commitments.
The current simulations follow ordinary chronological FTP through investments and payments. The next study will connect that member experience with the continuation work and a settlement policy for retained assets.
Papers, calculations and verification · An interactive transfer example.
From the rule to the calculation
The Fair Tontine Engine is the implementation of the fair transfer plan used in this research. Its worked examples show how allocations are calculated and checked for heterogeneous members.