Comparison theorem and its applications to finance

• Author / Creator

  Krasin, Vladislav

• The current Thesis is devoted to comprehensive studies of comparison, or stochastic domination, theorems. It presents a combination of theoretical research and practical ideas formulated in several specific examples. Previously known results and their place it the theory of stochastic processes and stochastic differential equations is reviewed. This part of the work yielded three new theoretical results, formulated as theorems. Two of them are extensions of commonly used methods to more sophisticated processes and conditions. The third theorem is proven using previously not exploited technique. The place of all three results in the global theory is demonstrated by examining interconnections and possible distinctions between old and new theorems. Second and equally important part of the work focuses on more practical
  issues. Its main goal is to demonstrate where and how various theoretical findings can be applied to typical financial problems, such as option pricing,
  hedging, risk management and others. The example chapter summarizes the best of the obtained results in this direction.

• Subjects / Keywords

  • Mathematical finance, stochastic differential equations, comparison theorem

• Graduation date

  Fall 2010

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R39K5D

• 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.