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Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Rauhe Pfade und Rauhe Volatilität
No full textIn this thesis we treat two separate topics relating to rough analysis: Rough differential equations and rough volatility models. The first part of the thesis presents a novel adaptive algorithm based on the log-ODE method for efficiently solving rough differential equations. The second, third and fourth part discusses Markovian approximation of rough volatility models, with a particular focus on the rough Heston model.
More precisely, in the first part of this thesis we present an adaptive algorithm for effectively solving rough differential equations (RDEs) using the log-ODE method. The algorithm is based on an error representation formula that accurately describes the contribution of local errors to the global error. By incorporating a cost model, our algorithm efficiently determines whether to refine the time grid or increase the order of the log-ODE method. Several illustrative examples underscore the efficacy of this adaptive approach for solving RDEs.
In the second part we consider rough stochastic volatility models where the variance process satisfies a stochastic Volterra equation with the fractional kernel, as in the rough Bergomi and the rough Heston model. In particular, these rough volatility models fail to be Markov processes or semimartingales, which poses significant theoretical and practical challenges. To remedy this, we study approximations of stochastic Volterra equations using an N-dimensional diffusion process defined as solution to a system of ordinary stochastic differential equation. If the coefficients of the stochastic Volterra equation are Lipschitz continuous, we show that these approximations converge strongly with super-polynomial rate in N. Finally, we apply this approximation to compute the implied volatility smile of a European call option under the rough Bergomi and the rough Heston model.
In the third part we continue our study of Markovian approximations for the specific case of the rough Heston model. Existing error analysis, including the second part of this thesis, is largely based on the strong error, corresponding to the L^2 distance between the kernels. Extending earlier results by \cite{abi2019multifactor}, we show that the weak error of the Markovian approximations can be bounded using the L^1-error in the kernel approximation for general classes of payoff functions for European style options. Moreover, we give specific Markovian approximations which converge super-polynomially in the number of dimensions, and illustrate their numerical superiority in option pricing compared to previously existing approximations, including those in the second part. The new approximations also work for the hyper-rough case H > -1/2.
In the fourth part we provide an efficient and accurate simulation scheme for the rough Heston model in the standard (H>0) as well as the hyper-rough regime (H > -1/2). The scheme is based on the low-dimensional Markovian approximations of the third part of this thesis, yielding weak approximations of the rough Heston process. Numerical experiments show that the new scheme exhibits second order weak convergence, while the computational cost increases linearly with respect to the number of time steps. In contrast, existing schemes based on discretization of underlying stochastic Volterra integrals, such as Gatheral's HQE scheme, exhibit a quadratic computational cost. Extensive numerical tests for European and Bermudan options illustrate the method's accuracy and efficiency.In dieser Arbeit behandeln wir zwei separate Themen im Zusammenhang mit rauer Analysis: Raue Differentialgleichungen und raue Volatilitätsmodelle. Der erste Teil der Arbeit präsentiert einen neuartigen adaptiven Algorithmus basierend auf der Log-ODE-Methode, um raue Differentialgleichungen effizient zu lösen. Der zweite, dritte und vierte Teil diskutieren die Markow-Approximation von rauen Volatilitätsmodellen, wobei ein besonderer Fokus auf dem rauen Heston-Modell liegt.
Genauer gesagt präsentieren wir im ersten Teil dieser Arbeit einen adaptiven Algorithmus zur effektiven Lösung rauer Differentialgleichungen (RDEs) unter Verwendung der Log-ODE-Methode. Der Algorithmus basiert auf einer Fehlerdarstellung, die den Beitrag lokaler Fehler zum globalen Fehler beschreibt. Durch die Einbeziehung eines Kostenmodells bestimmt unser Algorithmus effizient, ob das Zeitgitter verfeinert oder die Ordnung der Log-ODE-Methode erhöht werden soll. Mehrere anschauliche Beispiele verdeutlichen die Wirksamkeit dieses adaptiven Ansatzes zur Lösung von RDEs.
Im zweiten Teil betrachten wir raue stochastische Volatilitätsmodelle, bei denen der Varianzprozess durch eine stochastische Volterra-Gleichung mit dem fraktionellen Kern gegeben ist, wie beim rauen Bergomi- und dem rauen Heston-Modell. Insbesondere sind diese rauen Volatilitätsmodelle keine Markow-Prozesse oder Semimartingale, was eine bedeutende theoretische und praktische Herausforderung darstellt. Um dies zu beheben, untersuchen wir Approximationen stochastischer Volterra-Gleichungen unter Verwendung eines N-dimensionalen Diffusionsprozesses, der als Lösung eines Systems gewöhnlicher stochastischer Differentialgleichungen definiert ist. Falls die Koeffizienten der stochastischen Volterra-Gleichung Lipschitz-stetig sind, zeigen wir, dass diese Approximationen stark mit einer super-polynomialen Rate in N konvergieren. Abschließend wenden wir diese Approximation auf die Berechnung des impliziten Volatilitäts-Smile einer europäischen Call-Option unter dem rauen Bergomi- und dem rauen Heston-Modell an.
Im dritten Teil setzen wir unsere Untersuchung von Markow-Approximationen für den speziellen Fall des rauen Heston-Modells fort. Die vorhandene Fehleranalyse, einschließlich des zweiten Teils dieser Arbeit, basiert weitgehend auf dem starken Fehler, der dem L^2-Abstand zwischen den Kernen entspricht. Unter Erweiterung früherer Ergebnisse von \cite{abi2019multifactor} zeigen wir, dass der schwache Fehler der Markow-Approximationen für allgemeine Klassen von Auszahlungsfunktionen für europäische Optionen mit dem L^1-Fehler in der Kernapproximation begrenzt werden kann. Außerdem geben wir spezifische Markow-Approximationen an, die in der Anzahl der Dimensionen superpolynomiell konvergieren, und veranschaulichen ihre numerische Überlegenheit für die Berechnung von Optionspreisen im Vergleich zu bisherigen Approximationen, einschließlich derer im zweiten Teil. Die neuen Approximationen funktionieren auch für den hyper-rauen Fall H > -1/2.
Im vierten Teil bieten wir ein effizientes und genaues Simulationsverfahren für das raue Heston-Modell im Standardfall (H > 0) sowie im hyper-rauen Regime (H > -1/2). Das Verfahren basiert auf den niedrigdimensionalen Markow-Approximationen des dritten Teils dieser Arbeit und liefert schwache Approximationen des rauen Heston-Prozesses. Numerische Experimente zeigen, dass das neue Verfahren eine schwache Konvergenz zweiter Ordnung aufweist, während die Rechenkosten linear mit der Anzahl der Zeitschritte steigen. Im Gegensatz dazu weisen bestehende Verfahren, die auf der Diskretisierung der zugrunde liegenden stochastischen Volterra-Gleichung basieren, wie Gatherals HQE-Verfahren, eine quadratische Rechenkomplexität auf. Umfangreiche numerische Tests für europäische und Bermuda-Optionen verdeutlichen die Genauigkeit und Effizienz der Methode.DFG, 410208580, GRK 2544: Stochastische Analysis in Interaktio
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Pricing American options under rough Heston
No full textThe rough Heston model is a popular option pricing model in mathematical finance. However, due to the non-semimartingale and non-Markovian characteristics of its volatility process, simulations can be prohibitively expensive in practice. Building on previous works, we approximate the volatility process with an N-dimensional diffusion, yielding a Markovian approximation of the rough Heston model. Then, we introduce a weak discretization scheme to simulate paths of these Markovian approximations. Our numerical experiments show that these approximations converge at a second-order rate as the number of time steps approaches infinity. We leverage these approximations to price Bermudan options under the rough Heston model
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Functions of bounded variation in one and multiple dimensions
No full textIn this Masters thesis, we investigate the properties of functions of bounded variation. First, we consider univariate functions, afterwards we generalize this notion to higher dimensions. There are many different definitions of multivariate functions of bounded variation. We study functions of bounded variation in the senses of Vitali; Hardy and Krause; Arzelà; and Hahn. Many results for those functions of bounded variation were previously only known in the bivariate case. We extend them to arbitrary dimensions, and also add some new results.eingereicht von Simon BreneisMasterarbeit Universität Linz 202
Journal of mathematical Analysis and Applications / On variation functions and their moduli of continuity
No full textWe study the moduli of continuity of functions of bounded variation and of their variation functions. It is easy to see that the modulus of continuity of a function of bounded variation is always smaller or equal to the modulus of continuity of its variation function. We show that we cannot make any reasonable conclusion on the modulus of continuity of the variation function if we only know the modulus of continuity of the parent function itself. In particular, given two moduli of continuity, the first being weaker than Lipschitz continuity, we show that there exists a function of bounded variation with minimal modulus of continuity less than the first modulus of continuity, but with a variation function with minimal modulus of continuity greater than the second modulus of continuity. In particular, this negatively resolves the open problem whether the variation function of an α-Hölder continuous function is α-Hölder continuous.Fonds zur Förderung der Wissenschaftlichen Forschung F5513-N26Version of recor
Functions of bounded variation in one and multiple dimensions
No full textIn this Masters thesis, we investigate the properties of functions of bounded variation. First, we consider univariate functions, afterwards we generalize this notion to higher dimensions. There are many different definitions of multivariate functions of bounded variation. We study functions of bounded variation in the senses of Vitali; Hardy and Krause; Arzelà; and Hahn. Many results for those functions of bounded variation were previously only known in the bivariate case. We extend them to arbitrary dimensions, and also add some new results.eingereicht von Simon BreneisMasterarbeit Universität Linz 202
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