  Motivated by a new formulation of the classical dividend problem, we show
that Peskir's maximality principle can be transferred to singular stochastic
control problems with 2-dimensional degenerate dynamics and absorption along
the diagonal of the state space. We construct an optimal control as a Skorokhod
reflection along a moving barrier, where the barrier can be computed
analytically as the smallest solution to a certain non-linear ordinary
differential equation. Contrarily to the classical 1-dimensional formulation of
the dividend problem, our framework produces a non-trivial solution when the
firm's (pre-dividend) equity capital evolves as a geometric Brownian motion.
Such solution is also qualitatively different from the one traditionally
obtained for the arithmetic Brownian motion.
