  We solve a problem of singular stochastic control with discretionary
stopping, suggested as an interesting open problem by Karatzas, Ocone, Wang and
Zervos (2000), by providing suitable candidates for the moving boundaries in an
unsolved parameter range. We proceed by identifying an optimal stopping problem
with similar variational inequalities and inspecting its parameter-dependent
geometry (in a sense going back to Dynkin (1965)), which reveals a
discontinuity not previously exploited. We thus highlight the potential
importance of this geometric information in both singular control and
parameter-dependent optimal stopping.
