Continuous-time Duality for Super-replication with Transient Price Impact
Abstract
We establish a super-replication duality in a continuous-time financial model where an investor's trades adversely affect bid- and ask-prices for a risky asset and where market resilience drives the resulting spread back towards zero at an exponential rate. Similar to the literature on models with a constant spread, our dual description of super-replication prices involves the construction of suitable absolutely continuous measures with martingales close to the unaffected reference price. A novel feature in our duality is a liquidity weighted -norm that enters as a measurement of this closeness and that accounts for strategy dependent spreads. As applications, we establish optimality of buy-and-hold strategies for the super-replication of call options and we prove a verification theorem for utility maximizing investment strategies.
Keywords
Cite
@article{arxiv.1808.09807,
title = {Continuous-time Duality for Super-replication with Transient Price Impact},
author = {Peter Bank and Yan Dolinsky},
journal= {arXiv preprint arXiv:1808.09807},
year = {2019}
}