Asset Pricing with General Transaction Costs: Theory and Numerics

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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 wellposedness results, but can be solved numerically using the simulation-based deep-learning approach of Han, Jentzen and E (2018).