Asset Pricing with General Transaction Costs: Theory and Numerics
Abstract
We study risksharing equilibria with general convex costs on the agents' trading rates. For an infinitehorizon model with linear state dynamics and exogenous volatilities, the equilibrium returns meanrevert around their frictionless counterparts  the deviation has OrnsteinUhlenbeck dynamics for quadratic costs whereas it follows a doublyreflected Brownian motion if costs are proportional. More general models with arbitrary state dynamics and endogenous volatilities lead to multidimensional systems of nonlinear, fullycoupled forwardbackward SDEs. These fall outside the scope of known wellposedness results, but can be solved numerically using the simulationbased deeplearning approach of \cite{han.al.17}. In a calibration to time series of returns, bidask spreads, and trading volume, transaction costs substantially affect equilibrium asset prices. In contrast, the effects of different cost specifications are rather similar, justifying the use of quadratic costs as a proxy for other less tractable specifications.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.05027
 Bibcode:
 2019arXiv190505027G
 Keywords:

 Quantitative Finance  Mathematical Finance;
 91G10;
 91G80;
 60H10