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Motivated by a new formulation of the classical dividend problem, we showthat Peskir's maximality principle can be transferred to singular stochasticcontrol problems with 2-dimensional degenerate dynamics and absorption alongthe diagonal of the state space. We construct an optimal control as a Skorokhodreflection along a moving barrier, where the barrier can be computedanalytically as the smallest solution to a certain non-linear ordinarydifferential equation. Contrarily to the classical 1-dimensional formulation ofthe dividend problem, our framework produces a non-trivial solution when thefirm's (pre-dividend) equity capital evolves as a geometric Brownian motion.Such solution is also qualitatively different from the one traditionallyobtained for the arithmetic Brownian motion.

The maximality principle in singular control with absorption and its applications to the dividend problem