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