Asset pricing with general transaction costs: Theory and numerics

We study risk‐sharing equilibria with general convex costs on the agents' trading rates. For an infinite‐horizon model with linear state dynamics and exogenous volatilities, we prove that the equilibrium returns mean‐revert around their frictionless counterparts—the deviation has Ornstein‐Uhlenbeck dynamics for quadratic costs whereas it follows a doubly‐reflected Brownian motion if costs are proportional. More general models with arbitrary state dynamics and endogenous volatilities lead to multidimensional systems of nonlinear, fully‐coupled forward‐backward SDEs. These fall outside the scope of known well‐posedness results, but can be solved numerically using the simulation‐based deep‐learning approach of Han, Jentzen, and E (2018). In a calibration to time series of prices and trading volume, realistic liquidity premia are accompanied by a moderate increase in volatility. The effects of different cost specifications are rather similar, justifying the use of quadratic costs as a proxy for other less tractable specifications.