We explicitly solve for the optimal dynamic strategy between a riskless asset and a risky asset with momentum. The optimal portfolio weight depends not only on momentum that characterizes the expected return as in Merton (1971) framework, but also on the historical price path, unlike in Merton....

To capture the well documented time series momentum and reversal in asset price, we develop a continuous-time asset price model, derive the optimal investment strategy theoretically, and test the strategy empirically. We show that, by combining market fundamentals and timing opportunity with...