  We study risk-sharing economies where heterogenous agents trade subject to
quadratic transaction costs. The corresponding equilibrium asset prices and
trading strategies are characterised by a system of nonlinear, fully-coupled
forward-backward stochastic differential equations. We show that a unique
solution generally exists provided that the agents' preferences are
sufficiently similar. In a benchmark specification with linear state dynamics,
the illiquidity discounts and liquidity premia observed empirically correspond
to a positive relationship between transaction costs and volatility.
