标题： 论最佳退休（如何提前退休） 显示英文标题

标题： On Optimal Retirement (How to Retire Early)

摘要： 我们提出一个最优控制问题，该问题源于一种可能新的退休投资模型。 给定一个控制函数$f$和我们的当前净值为$X(t)$对于任何$t$，我们将金额$f(X(t))$投资于市场。 我们需要拥有$M$"超级美元" 才能退休，并希望尽可能早地退休。 我们通过伊藤过程$dX(t)= (1+f(X(t))dt+ f(X(t))dW(t)$来模拟我们在每个无限小时间间隔内的净值变化。 我们说明如何选择最优的$f=f_0$并证明在所有非前瞻投资策略中，$f_0$的选择是最优的，而不仅仅是在马尔可夫策略中。 显示英文摘要

摘要： 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.