We study a risk-sharing economy in continuous time, where heterogeneous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of fully-coupled forward-backward stochastic differential equations (FBSDEs). These FBSDEs are linear in the case of exogenous volatilities and nonlinear in the case of endogenous volatilities. 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. The corresponding liquidity premia compared to the frictionless case are mean reverting; they are positive if the more risk-averse agents are net sellers. We conclude the talk by considering the welfare effects of transaction costs for both agents and discuss the implications for the potential introduction of a financial transaction tax. The talk is based on joint works with Bruno Bouchard, Masaaki Fukasawa, Gechun Liang, Johannes Muhle-Karbe, Dylan Possama ̈ı, and my PhD student Osian Shelley.