  We prove the global existence of an incomplete, continuous-time finite-agent
Radner equilibrium in which exponential agents optimize their expected utility
over both running consumption and terminal wealth. The market consists of a
traded annuity, and, along with unspanned income, the market is incomplete. Set
in a Brownian framework, the income is driven by a multidimensional diffusion,
and, in particular, includes mean-reverting dynamics.
  The equilibrium is characterized by a system of fully coupled quadratic
backward stochastic differential equations, a solution to which is proved to
exist under Markovian assumptions.
