Arbitrage and deflators in illiquid markets

Authors: Teemu Pennanen

Publish Date: 2009/12/09

Volume: 15, Issue: 1, Pages: 57-83

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Abstract

This paper presents a stochastic model for discretetime trading in financial markets where trading costs are given by convex cost functions and portfolios are constrained by convex sets The model does not assume the existence of a cash account/numeraire In addition to classical frictionless markets and markets with transaction costs or bid–ask spreads our framework covers markets with nonlinear illiquidity effects for large instantaneous trades In the presence of nonlinearities the classical notion of arbitrage turns out to have two equally meaningful generalizations a marginal and a scalable one We study their relations to state price deflators by analyzing two auxiliary market models describing the local and global behavior of the cost functions and constraints

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