The Annals of Applied Probability

Super-replication with nonlinear transaction costs and volatility uncertainty

Peter Bank, Yan Dolinsky, and Selim Gökay

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Abstract

We study super-replication of contingent claims in an illiquid market with model uncertainty. Illiquidity is captured by nonlinear transaction costs in discrete time and model uncertainty arises as our only assumption on stock price returns is that they are in a range specified by fixed volatility bounds. We provide a dual characterization of super-replication prices as a supremum of penalized expectations for the contingent claim’s payoff. We also describe the scaling limit of this dual representation when the number of trading periods increases to infinity. Hence, this paper complements the results in [Finance Stoch. 17 (2013) 447–475] and [Ann. Appl. Probab. 5 (1995) 198–221] for the case of model uncertainty.

Article information

Source
Ann. Appl. Probab., Volume 26, Number 3 (2016), 1698-1726.

Dates
Received: November 2014
Revised: June 2015
First available in Project Euclid: 14 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1465905016

Digital Object Identifier
doi:10.1214/15-AAP1130

Mathematical Reviews number (MathSciNet)
MR3513603

Zentralblatt MATH identifier
06618839

Subjects
Primary: 91G10: Portfolio theory 91G40: Credit risk

Keywords
Super-replication hedging with friction volatility uncertainty limit theorems

Citation

Bank, Peter; Dolinsky, Yan; Gökay, Selim. Super-replication with nonlinear transaction costs and volatility uncertainty. Ann. Appl. Probab. 26 (2016), no. 3, 1698--1726. doi:10.1214/15-AAP1130. https://projecteuclid.org/euclid.aoap/1465905016


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