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This paper treats a problem of determining the efficient frontier for the terminal wealth resulting from continuous investing policies over a finite time-interval. The underlying asset prices are driven by a jump-diffusion process. This is a generalization of the case considered by Zhou and Li (2000), where only the diffusion component is treated. Jumps need to be included to make the asset price model more representative of the behavior of real prices. To account for the jumps in the solution of this stochastic optimal control problem, a more general technique needs to be employed. It is based on characterization of the infinitesimal generator and the method of indeterminate coefficients to find the optimal value function and optimal control for each point on the efficient frontier. The results are illustrated with a numerical example.