Trading with Small Nonlinear Price Impact
41 Pages Posted:
Date Written: July 9, 2018
We study portfolio choice with small nonlinear price impact on general market dynamics. Using probabilistic techniques and convex duality, we show that the asymptotic optimum can be described explicitly up to the solution of a nonlinear ODE, which identifies the optimal trading speed and the performance loss due to the trading friction. Previous asymptotic results for proportional and quadratic trading costs are obtained as limiting cases. As an illustration, we discuss how nonlinear trading costs affect the pricing and hedging of derivative securities and active portfolio management.
Keywords: Nonlinear Price Impact, Portfolio Choice, Asymptotics
JEL Classification: G11, G12
Suggested Citation: Suggested Citation