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

  • NUPBR
  • Viability
  • Arbitrage
  • Informational Markets
  • Structure Conditions
  • Utility Maximization
  • Enlargement of Filtration
  • Semi-martingale

• Graduation date

  Fall 2014

• 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.