  We study a class of infinite-dimensional singular stochastic control problems
with applications in economic theory and finance. The control process linearly
affects an abstract evolution equation on a suitable partially-ordered
infinite-dimensional space X, it takes values in the positive cone of X, and it
has right-continuous and nondecreasing paths. We first provide a rigorous
formulation of the problem by properly defining the controlled dynamics and
integrals with respect to the control process. We then exploit the concave
structure of our problem and derive necessary and sufficient first-order
conditions for optimality. The latter are finally exploited in a specification
of the model where we find an explicit expression of the optimal control. The
techniques used are those of semigroup theory, vector-valued integration,
convex analysis, and general theory of stochastic processes.
