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 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 Itô process dX(t) = (1 + f(X(t)))dt + f(X(t))dW(t). We show how to choose the optimal f = f0 and show that the choice of f0 is optimal among all nonanticipative investment strategies, not just among Markovian ones.
Citation
Philip A. Ernst. Dean P. Foster. Larry A. Shepp. "On optimal retirement." J. Appl. Probab. 51 (2) 333 - 345, June 2014. https://doi.org/10.1239/jap/1402578628
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