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Sticky Continuous Processes have Consistent Price Systems

Part of: Stochastic processes Mathematical finance

Published online by Cambridge University Press:  30 January 2018

Christian Bender ,
Mikko S. Pakkanen  and
Hasanjan Sayit
Christian Bender*
Affiliation:
Saarland University
Mikko S. Pakkanen*
Affiliation:
Aarhus University and CREATES
Hasanjan Sayit*
Affiliation:
Durham University
*
∗ Postal address: Department of Mathematics, Saarland University, Postfach 151150, D-66041 Saarbrücken, Germany. Email address: bender@math.uni-sb.de
∗∗ Postal address: Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK. Email address: m.pakkanen@imperial.ac.uk
∗∗∗ Postal address: Department of Mathematical Sciences, Durham University, South Road, Durham DH1 3LE, UK. Email address: hasanjan.sayit@durham.ac.uk
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Abstract

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Under proportional transaction costs, a price process is said to have a consistent price system, if there is a semimartingale with an equivalent martingale measure that evolves within the bid-ask spread. We show that a continuous, multi-asset price process has a consistent price system, under arbitrarily small proportional transaction costs, if it satisfies a natural multi-dimensional generalization of the stickiness condition introduced by Guasoni (2006).

Keywords

Consistent price systemstickinessmartingalearbitragetransaction costs

MSC classification

Primary: 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
Secondary: 60G44: Martingales with continuous parameter
Type
Research Article
Information
Journal of Applied Probability , Volume 52 , Issue 2 , June 2015 , pp. 586 - 594
Copyright
© Applied Probability Trust 

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