Continuous-time duality for superreplication with transient price impact

Peter Bank, Yan Dolinsky

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

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 L2-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.

Original languageAmerican English
Pages (from-to)3893-3917
Number of pages25
JournalAnnals of Applied Probability
Volume29
Issue number6
DOIs
StatePublished - 2019

Bibliographical note

Publisher Copyright:
© Institute of Mathematical Statistics, 2019

Keywords

  • Consistent price systems
  • Duality
  • Permanent and transient price impact
  • Shadow price
  • Superreplication

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