We prove the uniqueness of an equilibrium solution to a general time-inconsistent LQ control problem under mild conditions which ensure the existence of a solution. This is the first positive result on the uniqueness of the solution to a time inconsistent dynamic decision problem in continuous-time setting. Key words. time-inconsistency, stochastic linear-quadratic control, uniqueness of equilibrium control, ] forward--backward stochastic differential equation, mean--variance portfolio selection  .
In this paper, we continue our study on a general time-inconsistent stochastic linear--quadratic (LQ) control problem originally formulated in 6]. We derive a necessary and sufficient condition for equilibrium controls via a flow of forward--backward stochastic differential equations. When the state is one dimensional and the coefficients in the problem are all deterministic, we prove that the explicit equilibrium control constructed in \mbox{%DIFAUXCMD HJZ mean--variance portfolio selection model in a complete financial market where the risk-free rate is a deterministic function of time but all the other market parameters are possibly stochastic processes .
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We prove the uniqueness of an equilibrium solution to
In this paper, we continue our study on
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LQ control problem under mild conditions which ensure the existence of a solution. This is the first positive result on the uniqueness of the solution to a time inconsistent dynamic decision problem in continuous-time setting. Key words. time-inconsistency, stochastic linear-quadratic control, uniqueness of equilibrium control,
stochastic linear--quadratic (LQ) control problem originally formulated in
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6
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. We derive a necessary and sufficient condition for equilibrium controls via a flow of
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stochastic differential equation,
stochastic differential equations. When the state is one dimensional and the coefficients in the problem are all deterministic, we prove that the explicit equilibrium control constructed in \mbox{%DIFAUXCMD HJZ
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model in a complete financial market where the risk-free rate is a deterministic function of time but all the other market parameters are possibly stochastic processes