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Comparison theorem and its applications to finance Open Access


Other title
Mathematical finance, stochastic differential equations, comparison theorem
Type of item
Degree grantor
University of Alberta
Author or creator
Krasin, Vladislav
Supervisor and department
Melnikov, Alexander (mathematical and statistical sciences)
Examining committee member and department
Schmuland, Byron (mathematical and statistical sciences)
Swishchuk, Anatoly (University of Calgary)
Cadenillas, Abel (mathematical and statistical sciences)
Szepesvari, Csaba (Computing science)
Choulli, Tahir (mathematical and statistical sciences)
Department of Mathematical and Statistical Sciences

Date accepted
Graduation date
Doctor of Philosophy
Degree level
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.
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.
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