Arbitrage theory for non convex financial market models

We propose a unified approach where a security market is described by a liquidation value process. This allows to extend the frictionless models of the classical theory as well as the recent proportional transaction costs models to a larger class of financial markets with transaction costs including...

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Bibliographic Details
Published in:Stochastic processes and their applications 2017-10, Vol.127 (10), p.3331-3353
Main Authors: Lepinette, Emmanuel, Tran, Tuan
Format: Article
Language:English
Subjects:
Arbitrage theory
European options
Liquidation value
Mathematics
Probability
Transaction costs
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Summary:We propose a unified approach where a security market is described by a liquidation value process. This allows to extend the frictionless models of the classical theory as well as the recent proportional transaction costs models to a larger class of financial markets with transaction costs including non proportional trading costs. The usual tools from convex analysis however become inadequate to characterize the absence of arbitrage opportunities in non-convex financial market models. The natural question is to which extent the results of the classical arbitrage theory are still valid. Our contribution is a first attempt to characterize the absence of arbitrage opportunities in non convex financial market models.
ISSN:0304-4149
1879-209X
DOI:10.1016/j.spa.2017.01.011