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We examine the optimal trading strategy for a CRRA investor who maximizes the expected utility of wealth on a finite date and faces transaction costs. Closed-form solutions are obtained when this date is uncertain. We then show a sequence of analytical solutions converge to the solution to the problem with a deterministic finite horizon. Consistent with the common life-cycle investment advice, the optimal trading strategy is found to be horizon dependent and largely buy and hold. Moreover, it might be optimal for the investor in our model not to buy any stock, even when the risk premium is positive. Further analysis of the optimal policy is also provided. Much of this work was completed while M. Loewenstein was at Washington University in St. Louis. We are grateful to an anonymous referee for useful suggestions. We also thank Jerome Detemple, Phil Dybvig, Gary Gorton

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