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A continuous-time Markowitz's mean-variance portfolio selection problem is studied in a market with one stock, one bond, and proportional transaction costs. This is a singular stochastic control problem, inherently with a finite time horizon. Via a series of transformations, the problem is turned into a so-called double obstacle problem, a well-studied problem in physics and PDE literature, featuring two time-varying free boundaries. The two boundaries, which define the buy, sell, and no-trade regions, are proved to be smooth in time. This in turn characterizes the optimal strategy, via a Skorokhod problem, as one that tries to keep a certain adjusted bond-stock position within the no-trade region. Several features of the optimal strategy are revealed that are remarkably different from its no-transaction-cost counterpart. It is shown that there exists a critical length in time, which is dependent on the stock excess return as well …