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Essays on Arbitrage Theory for a Class of Informational Markets Open Access


Other title
Structure Conditions
Informational Markets
Utility Maximization
Enlargement of Filtration
Type of item
Degree grantor
University of Alberta
Author or creator
Deng, Jun
Supervisor and department
Tahir, Choulli (Department of Mathematical and Statistical Sciences)
Examining committee member and department
Dmitry, Kramkov (Department of Mathematical Sciences, Carnegie Mellon University)
Byron, Schmuland (Department of Mathematical and Statistical Sciences)
Naomi, Rothenberg (Alberta School of Business)
Tahir, Choulli (Department of Mathematical and Statistical Sciences)
Rohana, Karunamuni (Department of Mathematical and Statistical Sciences)
Christoph, Frei (Department of Mathematical and Statistical Sciences)
Abel, Cadenillas (Department of Mathematical and Statistical Sciences)
Department of Mathematical and Statistical Sciences
Mathematical Finance
Date accepted
Graduation date
Doctor of Philosophy
Degree level
This thesis develops three major essays on Arbitrage Theory, Market’s Viabil- ity and Informational Markets. The first essay (Chapter 3) elaborates the exact connections among the No-Unbounded-Profit-with-Bounded-Risk (called NUPBR hereafter) condition, the existence of the numeraire portfolio, and market’s weak/lo- cal viability. These tight relationships together with the financial crisis become our principal financial/economic leitmotif for the development of the next essay. In the second essay (Chapter 4 – Chapter 6), we focus on quantifying with extreme precision the effect of some additional information/uncertainty on the non-arbitrage concepts. As a result, we describe the interplay of this extra informa- tion and the market’s parameters for these non-arbitrage concepts to be preserved. Herein, we focus on the classical no-arbitrage and the NUPBR condition. This study contains two main parts. In the first part of this essay (Chapter 4), we analyze prac- tical examples of market models and extra information/uncertainty, for which we construct explicit ”classical” arbitrage opportunities generated by the extra infor- mation/uncertainty. These examples are built in Brownian filtration and in Poisson filtration as well. The second part (Chapters 5 and 6) addresses the NUPBR con- dition in two different directions. On the one hand, we describe the pairs of market model and random time for which the resulting informational market model fulfills the NUPBR condition. On the other hand, we characterize the random time mod- els that preserve the NUPBR condition. These results are elaborated for general market models with special attention to practical models such as discrete-time and Levy market models. The last essay (Chapter 7) investigates the effect of additional information on the Structure Conditions. These conditions are the alternatives to the non-arbitrage and viability assumption in the Markowitz settings.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
Citation for previous publication
T. Choulli, J. Deng and J. Ma, “How non-arbitrage, viability and numeraire portfolio are related”, Accepted in Finance and Stochastics, 2014.A. Aksamit, T. Choulli, J. Deng, and M. Jeanblanc, “Arbitrages in a progressive enlargement setting”, Arbitrage, Credit and Informational Risks, Peking University Series in Mathematics Vol. 6, 55-88, 2014.

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File title: Introduction
File title: Essays on Arbitrage Theory for a Class of Informational Markets
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