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December 2019 Continuous-time duality for superreplication with transient price impact
Peter Bank, Yan Dolinsky
Ann. Appl. Probab. 29(6): 3893-3917 (December 2019). DOI: 10.1214/19-AAP1498


We establish a superreplication duality in a continuous-time financial model as in (Bank and Voß (2018)) 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 (cf., e.g., Math. Finance 6 (1996) 133–165; Ann. Appl. Probab. 20 (2010) 1341–1358; Ann. Appl. Probab. 27 (2017) 1414–1451), our dual description of superreplication 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 superreplication of call options and we prove a verification theorem for utility maximizing investment strategies.


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Peter Bank. Yan Dolinsky. "Continuous-time duality for superreplication with transient price impact." Ann. Appl. Probab. 29 (6) 3893 - 3917, December 2019.


Received: 1 August 2018; Revised: 1 February 2019; Published: December 2019
First available in Project Euclid: 7 January 2020

zbMATH: 07172349
MathSciNet: MR4047995
Digital Object Identifier: 10.1214/19-AAP1498

Primary: 91G10 , 91G20

Keywords: consistent price systems , Duality , permanent and transient price impact , shadow price , Superreplication

Rights: Copyright © 2019 Institute of Mathematical Statistics


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Vol.29 • No. 6 • December 2019
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