  We study a risk-sharing economy where an arbitrary number of heterogenous
agents trades an arbitrary number of risky assets subject to quadratic
transaction costs. For linear state dynamics, the forward-backward stochastic
differential equations characterizing equilibrium asset prices and trading
strategies in this context reduce to a system of matrix-valued Riccati
equations. We prove the existence of a unique global solution and provide
explicit asymptotic expansions that allow us to approximate the corresponding
equilibrium for small transaction costs. These tractable approximation formulas
make it feasible to calibrate the model to time series of prices and trading
volume, and to study the cross-section of liquidity premia earned by assets
with higher and lower trading costs. This is illustrated by an empirical case
study.
