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A study of maximum and minimum operators with applications to piecewise linear payoff functionsSeedat, Ebrahim January 2013 (has links)
The payoff functions of contingent claims (options) of one variable are prominent in Financial Economics and thus assume a fundamental role in option pricing theory. Some of these payoff functions are continuous, piecewise-defined and linear or affine. Such option payoff functions can be analysed in a useful way when they are represented in additive, Boolean normal, graphical and linear form. The issue of converting such payoff functions expressed in the additive, linear or graphical form into an equivalent Boolean normal form, has been considered by several authors for more than half-a-century to better-understand the role of such functions. One aspect of our study is to unify the foregoing different forms of representation, by creating algorithms that convert a payoff function expressed in graphical form into Boolean normal form and then into the additive form and vice versa. Applications of these algorithms are considered in a general theoretical sense and also in the context of specific option contracts wherever relevant. The use of these algorithms have yielded easy computation of the area enclosed by the graph of various functions using min and max operators in several ways, which, in our opinion, are important in option pricing. To summarise, this study effectively dealt with maximum and minimum operators from several perspectives
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On local cohomology and local homology based on an arbitrary supportSarria, Luis Alberto Alba 15 December 2015 (has links)
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Previous issue date: 2015-12-15 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This work develops the theories of local cohomology and local homology with respect to
an arbitrary set of ideals and generalises most of the important results from the classical
theories. It also introduces the category of quasi-holonomic D-modules and proves some
finiteness properties of local cohomology modules which generalise Lyubeznik's results
in some sense. / Este trabalho desenvolve as teorias de cohomologia e homologia locais com respeito
a um conjunto arbitrário de ideais e generaliza vários dos resultados importantes das
teorias clássicas. Também, introduz a categoria dos D-módulos quase-holônomos e
prova alguns resultados de finitude de cohomologia local que generalizam, em algum
sentido, os resultados de G. Lyubeznik.
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