866 research outputs found

    Analysis of Fourier transform valuation formulas and applications

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    The aim of this article is to provide a systematic analysis of the conditions such that Fourier transform valuation formulas are valid in a general framework; i.e. when the option has an arbitrary payoff function and depends on the path of the asset price process. An interplay between the conditions on the payoff function and the process arises naturally. We also extend these results to the multi-dimensional case, and discuss the calculation of Greeks by Fourier transform methods. As an application, we price options on the minimum of two assets in L\'evy and stochastic volatility models.Comment: 26 pages, 3 figures, to appear in Appl. Math. Financ

    The singular continuous diffraction measure of the Thue-Morse chain

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    The paradigm for singular continuous spectra in symbolic dynamics and in mathematical diffraction is provided by the Thue-Morse chain, in its realisation as a binary sequence with values in {±1}\{\pm 1\}. We revisit this example and derive a functional equation together with an explicit form of the corresponding singular continuous diffraction measure, which is related to the known representation as a Riesz product.Comment: 6 pages, 1 figure; revised and improved versio

    Does This Child Have Appendicitis?

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    Evaluation of abdominal pain in children can be difficult. Rapid, accurate diagnosis of appendicitis in children reduces the morbidity of this common cause of pediatric abdominal pain. Clinical evaluation may help identify (1) which children with abdominal pain and a likely diagnosis of appendicitis should undergo immediate surgical consultation for potential appendectomy and (2) which children with equivocal presentations of appendicitis should undergo further diagnostic evaluation

    Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall

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    We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the theory of circle maps (which we review briefly) imply that there are intervals of parameters where the waves in the cavity get concentrated in wave packets whose energy grows exponentially. Even if these intervals are dense for typical motions of the reflecting boundary, in the complement there is a positive measure set of parameters where the energy remains bounded.Comment: 34 pages LaTeX (revtex) with eps figures, PACS: 02.30.Jr, 42.15.-i, 42.60.Da, 42.65.Y

    Finite-Dimensional Approximations of Unstable Infinite-Dimensional Systems

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    On infinite-volume mixing

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    In the context of the long-standing issue of mixing in infinite ergodic theory, we introduce the idea of mixing for observables possessing an infinite-volume average. The idea is borrowed from statistical mechanics and appears to be relevant, at least for extended systems with a direct physical interpretation. We discuss the pros and cons of a few mathematical definitions that can be devised, testing them on a prototypical class of infinite measure-preserving dynamical systems, namely, the random walks.Comment: 34 pages, final version accepted by Communications in Mathematical Physics (some changes in Sect. 3 -- Prop. 3.1 in previous version was partially incorrect

    A sociological dilemma: race, segregation, and US sociology

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    US sociology has been historically segregated in that, at least until the 1960s, there were two distinct institutionally organized traditions of sociological thought – one black and one white. For the most part, however, dominant historiographies have been silent on that segregation and, at best, reproduce it when addressing the US sociological tradition. This is evident in the rarity with which scholars such as WEB Du Bois, E Franklin Frazier, Oliver Cromwell Cox, or other ‘African American Pioneers of Sociology’, as Saint-Arnaud calls them, are presented as core sociological voices within histories of the discipline. This article addresses the absence of African American sociologists from the US sociological canon and, further, discusses the implications of this absence for our understanding of core sociological concepts. With regard to the latter, the article focuses in particular on the debates around equality and emancipation and discusses the ways in which our understanding of these concepts could be extended by taking into account the work of African American sociologists and their different interpretations of core themes
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