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  • http://hdl.handle.net/10402/era.27739
  • Comparison theorem and its applications to finance
  • Krasin, Vladislav
  • English
  • Mathematical finance, stochastic differential equations, comparison theorem
  • Aug 11, 2010 7:34 PM
  • Thesis
  • English
  • Adobe PDF
  • 548191 bytes
  • 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.
  • Doctoral
  • Doctor of Philosophy
  • Department of Mathematical and Statistical Sciences
  • Fall 2010
  • Melnikov, Alexander (mathematical and statistical sciences)
  • Schmuland, Byron (mathematical and statistical sciences)
    Cadenillas, Abel (mathematical and statistical sciences)
    Choulli, Tahir (mathematical and statistical sciences)
    Szepesvari, Csaba (Computing science)
    Swishchuk, Anatoly (University of Calgary)