The 10 most recently published documents
The economic growth theory analyses which factors affect economic growth
and tries to analyze how it can last. A popular neoclassical growth model
is the Ramsey-Cass-Koopmans model, which aims to determine how much
of its income a nation or an economy should save in order to maximize its
welfare.
In this thesis, we present and analyze an extended capital accumulation equation of a spatial version of the Ramsey model, balancing diffusive and agglomerative effects. We model the capital mobility in space via a nonlocal
diffusion operator which allows for jumps of the capital stock from one lo-
cation to an other. Moreover, this operator smooths out heterogeneities in
the factor distributions slower, which generated a more realistic behavior of
capital flows. In addition to that, we introduce an endogenous productivity-
production operator which depends on time and on the capital distribution
in space. This operator models the technological progress of the economy.
The resulting mathematical model is an optimal control problem under a
semilinear parabolic integro-differential equation with initial and volume constraints, which are a nonlocal analog to local boundary conditions, and box-constraints on the state and the control variables. In this thesis, we consider
this problem on a bounded and unbounded spatial domain, in both cases with
a finite time horizon. We derive existence results of weak solutions for the
capital accumulation equations in both settings and we proof the existence
of a Ramsey equilibrium in the unbounded case. Moreover, we solve the
optimal control problem numerically and discuss the results in the economic
context.
This dissertation is dedicated to the analysis of the stabilty of portfolio risk and the impact of European regulation introducing risk based classifications for investment funds.
The first paper examines the relationship between portfolio size and the stability of mutual fund risk measures, presenting evidence for economies of scale in risk management. In a unique sample of 338 fund portfolios we find that the volatility of risk numbers decreases for larger funds. This finding holds for dispersion as well as tail risk measures. Further analyses across asset classes provide evidence for the robustness of the effect for balanced and fixed income portfolios. However, a size effect did not emerge for equity funds, suggesting that equity fund managers simply scale their strategy up as they grow. Analyses conducted on the differences in risk stability between tail risk measures and volatilities reveal that smaller funds show higher discrepancies in that respect. In contrast to the majority of prior studies on the basis of ex-post time series risk numbers, this study contributes to the literature by using ex-ante risk numbers based on the actual assets and de facto portfolio data.
The second paper examines the influence of European legislation regarding risk classification of mutual funds. We conduct analyses on a set of worldwide equity indices and find that a strategy based on the long term volatility as it is imposed by the Synthetic Risk Reward Indicator (SRRI) would lead to substantial variations in exposures ranging from short phases of very high leverage to long periods of under investments that would be required to keep the risk classes. In some cases, funds will be forced to migrate to higher risk classes due to limited means to reduce volatilities after crises events. In other cases they might have to migrate to lower risk classes or increase their leverage to ridiculous amounts. Overall, we find if the SRRI creates a binding mechanism for fund managers, it will create substantial interference with the core investment strategy and may incur substantial deviations from it. Fruthermore due to the forced migrations the SRRI degenerates to a passive indicator.
The third paper examines the impact of this volatility based fund classification on portfolio performance. Using historical data on equity indices we find initially that a strategy based on long term portfolio volatility, as it is imposed by the Synthetic Risk Reward Indicator (SRRI), yields better Sharpe Ratios (SRs) and Buy and Hold Returns (BHRs) for the investment strategies matching the risk classes. Accounting for the Fama-French factors reveals no significant alphas for the vast majority of the strategies. In our simulation study where volatility was modelled through a GJR(1,1) - model we find no significant difference in mean returns, but significantly lower SRs for the volatility based strategies. These results were confirmed in robustness checks using alternative models and timeframes. Overall we present evidence which suggests that neither the higher leverage induced by the SRRI nor the potential protection in downside markets does pay off on a risk adjusted basis.
Kartenschätze aus Italien
(2018)
Die Entdeckungen der Neuzeit sowie verbesserte Druckverfahren führten ab dem 16. Jahrhundert zu einem enormen Aufschwung der Kartographie. Gerade in Italien entstanden blühende kartographische Zentren mit exzellentem Ruf, die innerhalb kurzer Zeit große Fortschritte hinsichtlich Genauigkeit und Übersichtlichkeit machten. Aus dem der Universitätsbibliothek Trier vermachten Nachlass des Kartensammlers Fritz Hellwig werden drei repräsentative Beispiele vorgestellt.
The implicit power motive is one of the most researched motives in motivational
psychology—at least in adults. Children have rarely been subject to investigation and there
are virtually no results on behavioral and affective correlates of the implicit power motive in
children. As behavior and affect are important components of conceptual validation, the
empirical data in this dissertation focused on identifying three correlates, namely resource
control behavior (study 1), power stress (study 2), and persuasive behavior (study 3). In each
study, the implicit power motive was measured via the Picture Story Exercise, using an
adapted version for children. Children across samples were between 4 and 11 years old.
Results from study 1 and 2 showed that children’s power-related behavior corresponded with
evidence from adult samples: children with a high implicit power motive secure attractive
resources and show negative reactions to a thwarted attempt to exert influence. Study 3
contradicted existing evidence with adults in that children’s persuasive behavior was not
associated with nonverbal, but with verbal strategies of persuasion. Despite this inconsistency,
these results are, together with the validation of a child-friendly Picture Story Exercise
version, an important step into further investigating and confirming the concept of the implicit
power motive and how to measure it in children.
A matrix A is called completely positive if there exists an entrywise nonnegative matrix B such that A = BB^T. These matrices can be used to obtain convex reformulations of for example nonconvex quadratic or combinatorial problems. One of the main problems with completely positive matrices is checking whether a given matrix is completely positive. This is known to be NP-hard in general. rnrnFor a given matrix completely positive matrix A, it is nontrivial to find a cp-factorization A=BB^T with nonnegative B since this factorization would provide a certificate for the matrix to be completely positive. But this factorization is not only important for the membership to the completely positive cone, it can also be used to recover the solution of the underlying quadratic or combinatorial problem.rnrnIn addition, it is not a priori known how many columns are necessary to generate a cp-factorization for the given matrix. The minimal possible number of columns is called the cp-rank of A and so far it is still an open question how to derive the cp-rank for a given matrix. Some facts on completely positive matrices and the cp-rank will be given in Chapter 2.rnrnMoreover, in Chapter 6, we will see a factorization algorithm, which, for a given completely positive matrix A and a suitable starting point, computes the nonnegative factorization A=BB^T. The algorithm therefore returns a certificate for the matrix to be completely positive. As introduced in Chapter 3, the fundamental idea of the factorization algorithm is to start from an initial square factorization which is not necessarily entrywise nonnegative, and extend this factorization to a matrix for which the number of columns is greater than or equal to the cp-rank of A. Then it is the goal to transform this generated factorization into a cp-factorization.rnrnThis problem can be formulated as a nonconvex feasibility problem, as shown in Section 4.1, and solved by a method which is based on alternating projections, as proven in Chapter 6.rnrnOn the topic of alternating projections, a survey will be given in Chapter 5. Here we will see how to apply this technique to several types of sets like subspaces, convex sets, manifolds and semialgebraic sets. Furthermore, we will see some known facts on the convergence rate for alternating projections between these types of sets. Considering more than two sets yields the so called cyclic projections approach. Here some known facts for subspaces and convex sets will be shown. Moreover, we will see a new convergence result on cyclic projections among a sequence of manifolds in Section 5.4.rnrnIn the context of cp-factorizations, a local convergence result for the introduced algorithm will be given. This result is based on the known convergence for alternating projections between semialgebraic sets.rnrnTo obtain cp-facrorizations with this first method, it is necessary to solve a second order cone problem in every projection step, which is very costly. Therefore, in Section 6.2, we will see an additional heuristic extension, which improves the numerical performance of the algorithm. Extensive numerical tests in Chapter 7 will show that the factorization method is very fast in most instances. In addition, we will see how to derive a certificate for the matrix to be an element of the interior of the completely positive cone.rnrnAs a further application, this method can be extended to find a symmetric nonnegative matrix factorization, where we consider an additional low-rank constraint. Here again, the method to derive factorizations for completely positive matrices can be used, albeit with some further adjustments, introduced in Section 8.1. Moreover, we will see that even for the general case of deriving a nonnegative matrix factorization for a given rectangular matrix A, the key aspects of the completely positive factorization approach can be used. To this end, it becomes necessary to extend the idea of finding a completely positive factorization such that it can be used for rectangular matrices. This yields an applicable algorithm for nonnegative matrix factorization in Section 8.2.rnNumerical results for this approach will suggest that the presented algorithms and techniques to obtain completely positive matrix factorizations can be extended to general nonnegative factorization problems.
Die Dissertation untersucht den Anteil der Armutsthematik an der Etablierung des Kinos in Deutschland. Der Untersuchungsschwerpunkt konzentriert sich auf die Jahre 1907 bis 1913, einer entscheidenden Zeitspanne für die Institutionalisierung des Kinos als Medium sui generis. Ziel der Untersuchung ist es, anhand von Filmanalysen wiederkehrende Muster medialer Praktiken der kinematographischen Artikulation der Sozialen Frage zu eruieren und ihre thematische Relevanz bzw. ihren Anteil für die Etablierung des Kinos in Deutschland zu bestimmen. Im Fokus stehen die Medienprodukte, ihre Motivgestaltung und Inszenierungspraktiken.
We will consider discrete dynamical systems (X,T) which consist of a state space X and a linear operator T acting on X. Given a state x in X at time zero, its state at time n is determined by the n-th iteration T^n(x). We are interested in the long-term behaviour of this system, that means we want to know how the sequence (T^n (x))_(n in N) behaves for increasing n and x in X. In the first chapter, we will sum up the relevant definitions and results of linear dynamics. In particular, in topological dynamics the notions of hypercyclic, frequently hypercyclic and mixing operators will be presented. In the setting of measurable dynamics, the most important definitions will be those of weakly and strongly mixing operators. If U is an open set in the (extended) complex plane containing 0, we can define the Taylor shift operator on the space H(U) of functions f holomorphic in U as Tf(z) = (f(z)- f(0))/z if z is not equal to 0 and otherwise Tf(0) = f'(0). In the second chapter, we will start examining the Taylor shift on H(U) endowed with the topology of locally uniform convergence. Depending on the choice of U, we will study whether or not the Taylor shift is weakly or strongly mixing in the Gaussian sense. Next, we will consider Banach spaces of functions holomorphic on the unit disc D. The first section of this chapter will sum up the basic properties of Bergman and Hardy spaces in order to analyse the dynamical behaviour of the Taylor shift on these Banach spaces in the next part. In the third section, we study the space of Cauchy transforms of complex Borel measures on the unit circle first endowed with the quotient norm of the total variation and then with a weak-* topology. While the Taylor shift is not even hypercyclic in the first case, we show that it is mixing for the latter case. In Chapter 4, we will first introduce Bergman spaces A^p(U) for general open sets and provide approximation results which will be needed in the next chapter where we examine the Taylor shift on these spaces on its dynamical properties. In particular, for 1<=p<2 we will find sufficient conditions for the Taylor shift to be weakly mixing or strongly mixing in the Gaussian sense. For p>=2, we consider specific Cauchy transforms in order to determine open sets U such that the Taylor shift is mixing on A^p(U). In both sections, we will illustrate the results with appropriate examples. Finally, we apply our results to universal Taylor series. The results of Chapter 5 about the Taylor shift allow us to consider the behaviour of the partial sums of the Taylor expansion of functions in general Bergman spaces outside its disc of convergence.
Given a compact set K in R^d, the theory of extension operators examines the question, under which conditions on K, the linear and continuous restriction operators r_n:E^n(R^d)→E^n(K),f↦(∂^α f|_K)_{|α|≤n}, n in N_0 and r:E(R^d)→E(K),f↦(∂^α f|_K)_{α in N_0^d}, have a linear and continuous right inverse. This inverse is called extension operator and this problem is known as Whitney's extension problem, named after Hassler Whitney. In this context, E^n(K) respectively E(K) denote spaces of Whitney jets of order n respectively of infinite order. With E^n(R^d) and E(R^d), we denote the spaces of n-times respectively infinitely often continuously partially differentiable functions on R^d. Whitney already solved the question for finite order completely. He showed that it is always possible to construct a linear and continuous right inverse E_n for r_n. This work is concerned with the question of how the existence of a linear and continuous right inverse of r, fulfilling certain continuity estimates, can be characterized by properties of K. On E(K), we introduce a full real scale of generalized Whitney seminorms (|·|_{s,K})_{s≥0}, where |·|_{s,K} coincides with the classical Whitney seminorms for s in N_0. We equip also E(R^d) with a family (|·|_{s,L})_{s≥0} of those seminorms, where L shall be a a compact set with K in L-°. This family of seminorms on E(R^d) suffices to characterize the continuity properties of an extension operator E, since we can without loss of generality assume that E(E(K)) in D^s(L).
In Chapter 2, we introduce basic concepts and summarize the classical results of Whitney and Stein.
In Chapter 3, we modify the classical construction of Whitney's operators E_n and show that |E_n(·)|_{s,L}≤C|·|_{s,K} for s in[n,n+1).
In Chapter 4, we generalize a result of Frerick, Jordá and Wengenroth and show that LMI(1) for K implies the existence of an extension operator E without loss of derivatives, i.e. we have it fulfils |E(·)|_{s,L}≤C|·|_{s,K} for all s≥0. We show that a large class of self similar sets, which includes the Cantor set and the Sierpinski triangle, admits an extensions operator without loss of derivatives.
In Chapter 5 we generalize a result of Frerick, Jordá and Wengenroth and show that WLMI(r) for r≥1 implies the existence of a tame linear extension operator E having a homogeneous loss of derivatives, such that |E(·)|_{s,L}≤C|·|_{(r+ε)s,K} for all s≥0 and all ε>0.
In the last chapter we characterize the existence of an extension operator having an arbitrary loss of derivatives by the existence of measures on K.
Die Arbeit geht von der These aus, dass zwischen Webers Konzept einer verstehenden Soziologie und der materialen Studie "Die Protestantische Ethik und der Geist des Kapitalismus" (PE) eine Differenz in Form einer Mehrleistung auf Seiten der PE besteht. Diese Annahme fußt auf der Beobachtung, dass die PE verschiedene Perspektiven auf die Entstehung sinnhafter Handlungsorientierungen offeriert und sich gleichsam Strategien zu deren Plausibilisierung identifizieren lassen. Derartige Zusammenhänge wurden von Weber in den methodologischen Schriften scheinbar nur am Rande thematisiert und die entsprechenden Passagen erwecken den Eindruck, dass die Frage nach der Geschichtlichkeit der sinnhaften Handlungsorientierungen lediglich als Prämisse bzw. als Begründung für die Notwendigkeit einer verstehenden Sinnerfassung Beachtung findet. Diese Beobachtung bestimmt den weiteren Gang der Untersuchung und führte zu einem argumentativen Aufbau, welcher sich als Dreischritt beschreiben lässt: a) Eine Diskussion des Erklärungsprofils von Webers Konzept einer verstehenden Soziologie sowie Beispiele für vermutete Mehrleistungen auf Seiten der PE dienen zunächst der genaueren Explikation der identifizierten Problemstellung (vgl. Abschnitt I). Hierauf aufbauend erweisen sich mit Blick auf den aktuellen Forschungsstand b) jene Argumentationszusammenhänge der materialen Forschung als problematisch bzw. in ihrer logischen Beziehung zur Methodologie Webers als weiterhin ungeklärt, welche in Abschnitt I zunächst auf eine Mehrleistung auf Seiten der PE hindeuten. Hierbei zeigt eine gegenüberstellende Untersuchung von Vertretern von Einheitsthesen (vgl. Prewo 1979, Schluchter 1998, Collins 1986a) sowie Vertretern von Differenzthesen (vgl. v. Schelting 1934, Bendix 1964, Kalberg 2001), dass der aktuelle Diskussionsstand weiterhin durch offene Fragen und Unstimmigkeiten charakterisiert ist (vgl. Abschnitt II). Implizite Antworten auf diese Probleme des aktuellen Diskussionsstands lassen sich über c) einen erneuten rekonstruierenden Blick auf die in der PE enthaltenen Zusammenhänge und Plausibilisierungsstrategien gewinnen. Hier ist die Strategie doppelseitig angelegt: Für einen Teil der identifizierten Probleme ist es von besonderer Bedeutung, einen systematischen Einblick in die in der PE enthaltenen Zusammenhänge zu gewinnen (vgl. Abschnitt III). Die hierbei gewonnenen Erträge dienen als Grundlage zur adäquaten Rekonstruktion der methodischen Umsetzung und ermöglichen ein Verständnis davon, wie Weber die in den Fokus der Forschung gestellten Phänomene zu erklären suchte (vgl. Abschnitt IV).
Gegenstand der vorliegenden Arbeit ist die Untersuchung der Lexik der spätmittelalterlichen Luxemburger Rechnungsbücher unter der Prämisse der Urbanität. Da auf keine ausgearbeitete Methodik zurückgegriffen werden konnte, anhand derer eine Einteilung in für die Analyse relevante bzw. irrelevante Lexik vorgenommen werden konnte, wurde im Rahmen der Arbeit unter Rückgriff auf sprachwissenschaftliche und geschichtswissenschaftliche Konzepte eine eigene Methodik entwickelt. Auf deren Basis erfolgte die Anlage des Untersuchungskorpus' auf der Grundlage der von 1388-1500 fast lückenlos überlieferten Rechnungsbücher der Stadt Luxemburg mit dem Ziel der Analyse spezifisch urbaner Lexik. Bei der Analyse wurde schließlich eine dreifache Zielsetzung verfolgt: Einerseits die Untersuchung der Lexik mit Blick auf die Verteilung von types und tokens in als spezifisch urban definierten Domänen, andererseits die Anlage eines Glossars, das als textphilologisches Werkzeug als Hilfsmittel bei der Erschließung der Rechnungsbücher dienen soll. Daneben wurde ebenfalls auf die geschichtswissenschaftlichen Erkenntnisgewinne eingegangen, die durch die jeweilige Wortschatzanalyse realisiert werden konnten.
