Equilibrium asset pricing with transaction costs
by Martin Herdegen1, Johannes Muhle-Karbe2 and Dylan Possamaï3
1University of Warwick, Department of Statistics, Coventry, CV4 7AL, UK
(email: m.herdegen@warwick.ac.uk)
2Imperial College London, Department of Mathematics, London, SW7 1NE, UK
(email: j.muhle-karbe@imperial.ac.uk)
3ETH Zürich, Department of Mathematics, Rämistrasse 101, Zürich 8092, Switzerland
(email: dylan.possamai@math.ethz.ch)
Abstract
We study risk-sharing economies where heterogeneous agents trade subject to quadratic transaction costs. The corresponding equilibrium asset prices and trading strategies are characterised by a system of nonlinear, fully coupled forward-backward stochastic differential equations. We show that a unique solution exists provided that the agents' preferences are sufficiently similar. In a benchmark specification with linear state dynamics, the illiquidity discounts and liquidity premia observed empirically correspond to a positive relationship between transaction costs and volatility.
Key words:
Asset pricing, Radner equilibrium, Transaction costs, Forward-backward SDEs
JEL Classification: C68, D52, G11, G12
Mathematics Subject Classification (2010): 91G10, 91G80, 60H10