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arXiv · 1808.09807

Continuous-time Duality for Super-replication with Transient Price Impact

Peter Bank·Yan Dolinsky
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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 $L^2$-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.

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Peter Bank, Yan Dolinsky. 2018-08-29. Continuous-time Duality for Super-replication with Transient Price Impact. https://arxiv.org/abs/1808.09807

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