On Optimal Retirement (How to Retire Early)
Philip Ernst, Dean Foster, and Larry Shepp

TL;DR
This paper formulates and solves an optimal control problem for early retirement investment strategies, identifying the optimal investment function to minimize retirement time under stochastic market dynamics.
Contribution
It introduces a new model for retirement investing using stochastic control and derives the optimal investment strategy among all nonanticipative strategies.
Findings
Derived the optimal investment function $f_0$ for early retirement.
Proved the optimality of $f_0$ among all nonanticipative strategies.
Provided a mathematical framework for early retirement planning under uncertainty.
Abstract
We pose an optimal control problem arising in a perhaps new model for retirement investing. Given a control function and our current net worth as for any , we invest an amount in the market. We need a fortune of "superdollars" to retire and want to retire as early as possible. We model our change in net worth over each infinitesimal time interval by the Ito process . We show how to choose the optimal and show that the choice of is optimal among all nonanticipative investment strategies, not just among Markovian ones.
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Taxonomy
TopicsStochastic processes and financial applications · Economic theories and models · Insurance, Mortality, Demography, Risk Management
