Withdrawal Success Estimation

Abstract

Given a geometric Levy alpha-stable wealth process, a log-Levy alpha-stable lower bound is constructed for the terminal wealth of a regular investing schedule. Using a transformation, the lower bound is applied to a schedule of withdrawals occurring after an initial investment. As a result, an upper bound is described on the probability to complete a given schedule of withdrawals. For withdrawals of a constant amount at equidistant times, necessary conditions are given on the initial investment and parameters of the wealth process such that $k$ withdrawals can be made with 95% confidence. When the initial investment is in the S&P Composite Index and $2\leq k\leq 16$, then the initial investment must be at least $k$ times the amount of each withdrawal.