2Boston University, Department of Mathematics and Statistics
111 Cummington Street, Boston, MA 02215, USA
and Dublin City University, School of Mathematical Sciences
Glasnevin, Dublin 9, Ireland
(email: guasoni@bu.edu)
3
ETH Zürich, Departement für Mathematik, and Swiss Finance Institute
Rämistrasse 101, CH-8092 Zürich, Switzerland
(email: johannes.muhle-karbe@math.ethz.ch)
4
Universität Wien, Fakultät für Mathematik
Nordbergstrasse 15, A-1090 Wien, Austria
(email: walter.schachermayer@univie.ac.at)
Abstract In a market with one safe and one risky asset, an investor with a long horizon, constant investment opportunities, and constant relative risk aversion trades with small proportional transaction costs.We derive explicit formulas for the optimal investment policy, its implied welfare, liquidity premium, and trading volume. At the first order, the liquidity premium equals the spread, times share turnover, times a universal constant. Results are robust to consumption and finite horizons. We exploit the equivalence of the transaction cost market to another frictionless market, with a shadow risky asset, in which investment opportunities are stochastic. The shadow price is also found explicitly.