  We study singular stochastic control of a two dimensional stochastic
differential equation, where the first component is linear with random and
unbounded coefficients. We derive existence of an optimal relaxed control and
necessary conditions for optimality in the form of a mixed relaxed-singular
maximum principle in a global form. A motivating example is given in the form
of an optimal investment and consumption problem with transaction costs, where
we consider a portfolio with a continuum of bonds and where the portfolio
weights are modeled as measure-valued processes on the set of times to
maturity.
