On Optimal Retirement (How to Retire Early)
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=f0 and show that the choice of f0 is optimal among all nonanticipative investment strategies, not just among Markovian ones.
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