Illiquid financial market models and absence of arbitrage

We study financial market models with different liquidity effects. In the first part of this paper, we extend the short-term price impact model introduced by Rogers and Singh (2007) to a general semimartingale setup. We show the convergence of the discrete-time into the continuous-time modeling fram...

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Bibliographic Details
Published inBlätter (Deutsche Gesellschaft für Versicherungs- und Finanzmathematik) Vol. 30; no. 2; pp. 395 - 407
Main Author Jüttner, Matthias P.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.11.2009
Subjects
Mathematics
Mathematics and Statistics
Original Research Paper
Plant Genetics and Genomics
Probability Theory and Stochastic Processes
Quantitative Finance
Trading Strategy
Price Taker
Price Process
Market Model
Local Martingale
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Summary:We study financial market models with different liquidity effects. In the first part of this paper, we extend the short-term price impact model introduced by Rogers and Singh (2007) to a general semimartingale setup. We show the convergence of the discrete-time into the continuous-time modeling framework when trading times approach each other. In the second part, arbitrage opportunities in illiquid economies are considered, in particular a modification of the feedback effect model of Bank and Baum (2004). We demonstrate that a large trader cannot create wealth at no risk within this framework. Here we have to assume that the price process is described by a continuous semimartingale.
ISSN:1864-0281
1864-0303
DOI:10.1007/s11857-009-0090-6