Equilibrium Asset Pricing with Transaction Costs

Abstract

This thesis studies risk-sharing equilibria where trading is subject to transaction costs. In an infinite-horizon model with specific state dynamics and exogenous price volatility but general convex trading costs, we determine equilibrium prices and trading strategies in closed form and show how this allows us to calibrate the model to time-series datafor prices and trading volume. For more general state dynamics and endogenous volatilities, equilibria with transaction costs correspond to fully-coupled systemsof nonlinear forward-backward stochastic differential equations. We propose a simulation-based deep-learning algorithm that allows us to approximate the solution of such systems numerically. For quadratic trading costs and specific state dynamics, we complement this with a global wellposedness result. As a byproduct, the latter also yields explicit asymptotic expansions of the equilibrium for small transaction costs. These small-cost asymptotics formally extend to models with general state dynamics, transaction costs, and endogenous volatilities, leading to explicit asymptotic approximations of equilibrium prices with general trading costs.