  To improve the efficient frontier of the classical mean-variance model in
continuous time, we propose a varying terminal time mean-variance model with a
constraint on the mean value of the portfolio asset, which moves with the
varying terminal time. Using the embedding technique from stochastic optimal
control in continuous time and varying the terminal time, we determine an
optimal strategy and related deterministic terminal time for the model. Our
results suggest that doing so for an investment plan requires minimizing the
variance with a varying terminal time.
