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On Optimal Retirement (How to Retire Early)

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  • Philip Ernst
  • Dean Foster
  • Larry Shepp

Abstract

We pose an optimal control problem arising in a perhaps new model for retirement investing. Given a control function $f$ and our current net worth as $X(t)$ for any $t$, we invest an amount $f(X(t))$ in the market. We need a fortune of $M$ "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 $dX(t)= (1+f(X(t))dt+ f(X(t))dW(t)$. We show how to choose the optimal $f=f_0$ and show that the choice of $f_0$ is optimal among all nonanticipative investment strategies, not just among Markovian ones.

Suggested Citation

  • Philip Ernst & Dean Foster & Larry Shepp, 2016. "On Optimal Retirement (How to Retire Early)," Papers 1605.01028, arXiv.org.
    • Handle: RePEc:arx:papers:1605.01028
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    References listed on IDEAS

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    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    2. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    3. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
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