["Mathematical Finance, EarlyView. ", "\nABSTRACT\nThe optimal mean–variance selling problem seeks to determine a dynamically optimal stopping time in the nonlinear problem sup0≤τ≤TE(Xτ)−cVar(Xτ)$\\sup _{0 \\le \\tau \\le T} \\left[ \\mathsf {E}\\,\\!(X_\\tau) - c\\, \\mathsf {V}ar\\,\\!(X_\\tau) \\right]$, where X$X$ is a geometric Brownian motion with strictly positive drift, the supremum is taken over stopping times τ$\\tau$ of X$X$, and c>0$c>0$ is a given and fixed constant. The solution to the problem is known when the horizon T$T$ is infinite, however, the method of proof developed to solve the problem in that case is not applicable in the case when the horizon T$T$ is finite. In this paper, we develop a new method of proof, which solves the problem when the horizon T$T$ is finite. In this way, we find that the dynamically optimal stopping time is given by τ∗=inf{t≥0|Xt≥b(t)/(c(1−2b(t)))}$\\tau_* = \\inf \\:\\! \\{ \\, t \\ge 0 \\; \\vert \\; X_t \\ge b(t)/(c(1 \\! - \\! 2b(t))) \\, \\}$, where the function b$b$ can be characterized as a unique solution to a nonlinear Volterra integral equation. We also prove that the dynamically optimal stopping time τ∗$\\tau _*$ satisfies the smooth fit principle. To our knowledge, this is the first time that such a nonlinear phenomenon of “dynamic smooth fit” has been derived in the literature. MSC2020 Classification: 60G40, 35R35, 60J65, 90C30, 45G10, 91B06"]