Withdrawal Success Estimation

Abstract

Given an asset having a geometric Lévy alpha-stable wealth process, a log-Lévy 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 [Formula: see text] withdrawals can be made with 95% confidence. When withdrawing from an annually rebalanced portfolio maintaining 100[Formula: see text]% in the S&P Composite Index and 100([Formula: see text])% in inflation protected bonds, the initial investment must be at least [Formula: see text] times the amount of each withdrawal for [Formula: see text] and [Formula: see text].