Hedging, arbitrage and optimality with superlinear frictions

Abstract

In a continuous-time model with multiple assets described by càdlàg processes, this paper characterizes superhedging prices, absence of arbitrage, and utility maximizing strategies, under general frictions that make execution prices arbitrarily unfavorable for high trading intensity. Such frictions induce a duality between feasible trading strategies and shadow execution prices with a martingale measure. Utility maximizing strategies exist even if arbitrage is present, because it is not scalable at will.

Published at http://dx.doi.org/10.1214/14-AAP1043 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Consistent price systems and face-lifting pricing under transaction costs
• On using shadow prices in portfolio optimization with transaction costs