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Essays on Arbitrage Theory for a Class of Informational Markets

  • Author / Creator
    Deng, Jun
  • 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.

  • Subjects / Keywords
  • Graduation date
    2014-11
  • Type of Item
    Thesis
  • Degree
    Doctor of Philosophy
  • DOI
    https://doi.org/10.7939/R3KP7TZ24
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
    English
  • Institution
    University of Alberta
  • Degree level
    Doctoral
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematical Finance
  • Supervisor / co-supervisor and their department(s)
    • Tahir, Choulli (Department of Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Rohana, Karunamuni (Department of Mathematical and Statistical Sciences)
    • Naomi, Rothenberg (Alberta School of Business)
    • Christoph, Frei (Department of Mathematical and Statistical Sciences)
    • Abel, Cadenillas (Department of Mathematical and Statistical Sciences)
    • Byron, Schmuland (Department of Mathematical and Statistical Sciences)
    • Tahir, Choulli (Department of Mathematical and Statistical Sciences)
    • Dmitry, Kramkov (Department of Mathematical Sciences, Carnegie Mellon University)