Withdrawal Success Optimization

ArXiv ID: 2311.06665 “View on arXiv”

Authors: Unknown

Abstract

For $n$ assets and discrete-time rebalancing, the probability to complete a given schedule of investments and withdrawals is maximized over progressively measurable portfolio weight functions. Applications consider two assets, namely the S&P Composite Index and an inflation-protected bond. The maximum probability and optimal portfolio weight functions are computed for annually rebalanced schedules involving an arbitrary initial investment and then equal annual withdrawals over the remainder of the time period. Applications also consider annually rebalanced schedules that start with dollar cost averaging (equal annual investments) and then shift to equal annual withdrawals. Results indicate noticeable improvements in the probability to complete a given schedule when optimal portfolio weights are used instead of constant portfolio weights like the standard of keeping 90% in the S&P Composite Index and 10% in inflation-protected bonds.

Keywords: portfolio optimization, progressive measurability, dollar cost averaging, withdrawal scheduling, probability maximization, Portfolio Management (Lifecycle/Retirement)

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper utilizes advanced probability theory and stochastic calculus with progressively measurable processes and recursive formulas, indicating high mathematical density. Empirically, it provides concrete numerical improvements and confidence levels using S&P Composite Index and inflation-protected bond data, demonstrating backtest-ready methodology with specific asset implementations.

  flowchart TD
    A["Research Goal:<br>Maximize Withdrawal Success Probability<br>for Discrete-Time Rebalancing"] --> B["Methodology:<br>Optimize Progressively Measurable<br>Portfolio Weight Functions"]
    B --> C["Data Inputs:<br>S&P Composite Index &<br>Inflation-Protected Bond"]
    C --> D["Computational Process:<br>Analyze Schedules (Initial Investment +<br>Equal Annual Withdrawals / DCA)"]
    D --> E["Key Finding 1:<br>Optimal Weights Increase Probability<br>of Completing Schedule vs. Constant Weights"]
    D --> F["Key Finding 2:<br>Significant Improvements over<br>Standard 90/10 Portfolio Allocation"]