This paper addresses a continuous-time mean-variance portfolio selection model formulated as a bicriteria optimization problem, aiming to maximize the expected terminal return and minimize the variance of terminal wealth. By assigning weights to these two objectives, a single stochastic control problem is obtained, which is not in standard form due to the variance term. It is shown that this non-standard problem can be embedded into a class of auxiliary stochastic linear-quadratic (LQ) problems. The stochastic LQ control model provides an effective framework for studying the mean-variance problem, leveraging recent developments in general stochastic LQ problems with indefinite control weighting matrices. This leads to an efficient frontier in closed form for the original portfolio selection problem. The mean-variance approach, introduced by Markowitz, quantifies risk using variance and forms the basis of modern finance. However, its application in dynamic, multiperiod settings has been limited. In multiperiod models, maximizing expected utility functions of terminal wealth has dominated research, but this approach lacks the intuitive risk-return tradeoff of Markowitz's method. The paper highlights the difficulty of applying dynamic programming to objectives involving nonlinear utility functions, such as $ U[Ex(T)] $, due to the absence of a smoothing property. The mean-variance hedging problem has been studied with optimal hedging policies derived using the projection theorem, often under deterministic assumptions. The paper also discusses solving variance minimization problems with equality constraints on expected returns using the Lagrangian approach.This paper addresses a continuous-time mean-variance portfolio selection model formulated as a bicriteria optimization problem, aiming to maximize the expected terminal return and minimize the variance of terminal wealth. By assigning weights to these two objectives, a single stochastic control problem is obtained, which is not in standard form due to the variance term. It is shown that this non-standard problem can be embedded into a class of auxiliary stochastic linear-quadratic (LQ) problems. The stochastic LQ control model provides an effective framework for studying the mean-variance problem, leveraging recent developments in general stochastic LQ problems with indefinite control weighting matrices. This leads to an efficient frontier in closed form for the original portfolio selection problem. The mean-variance approach, introduced by Markowitz, quantifies risk using variance and forms the basis of modern finance. However, its application in dynamic, multiperiod settings has been limited. In multiperiod models, maximizing expected utility functions of terminal wealth has dominated research, but this approach lacks the intuitive risk-return tradeoff of Markowitz's method. The paper highlights the difficulty of applying dynamic programming to objectives involving nonlinear utility functions, such as $ U[Ex(T)] $, due to the absence of a smoothing property. The mean-variance hedging problem has been studied with optimal hedging policies derived using the projection theorem, often under deterministic assumptions. The paper also discusses solving variance minimization problems with equality constraints on expected returns using the Lagrangian approach.