  Consider a closed pooled annuity fund investing in n assets with
discrete-time rebalancing. At time 0, each annuitant makes an initial
contribution to the fund, committing to a predetermined schedule of
withdrawals. Require annuitants to be homogeneous in the sense that their
initial contributions and predetermined withdrawal schedules are identical, and
their mortality distributions are identical and independent. Under the
forementioned setup, the probability for a particular annuitant to complete the
prescribed withdrawals until death is maximized over progressively measurable
portfolio weight functions. Applications consider fund portfolios that mix two
assets: the S&P Composite Index and an inflation-protected bond. The maximum
probability is computed for annually rebalanced schedules consisting of an
initial investment and then equal annual withdrawals until death. A
considerable increase in the maximum probability is achieved by increasing the
number of annuitants initially in the pool. For example, when the per-annuitant
initial contribution and annual withdrawal amount are held constant, starting
with 20 annuitants instead of just 1 can increase the maximum probability
(measured on a scale from 0 to 1) by as much as .15.
