Date of Completion

6-17-2019

Embargo Period

6-18-2019

Keywords

Retirement Financial Planning, Kalman Filter, Geometric Brownian Motion, Markov Chain

Major Advisor

Jeyaraj Vadiveloo

Associate Advisor

Guojun Gan

Associate Advisor

Bin Zou

Field of Study

Mathematics

Degree

Doctor of Philosophy

Open Access

Open Access

Abstract

We developed a retirement financial planning strategy based on Markov chain modeling of retirement health conditions and Geometric Brownian Motion modeling of asset values. The annual living expenses of a retiree are modeled as basic expenses plus discretionary expenses. Our goal is to solve for the maximum discretionary expenses while healthy, which was obtained using a closed-form solution and quantile optimization technique. The highlight of this model is the use of Kalman Filter for annual recalibration. It allows the model to automatically adjust the suggested amount of discretionary expenses by looking at daily fund values from previous year. After running a lot of simulations and testings, we showed that our dynamic model beats other static models and a naive recalibration model in the sense that it virtually eliminates ruin and is able to let a retiree withdraw the largest possible amount.

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