Spectral bounds for singular indefinite Sturm-Liouville operators with L1L^1--potentials

The spectrum of the singular indefinite Sturm-Liouville operator $$A=\text{\rm sgn}(\cdot)\bigl(-\tfrac{d^2}{dx^2}+q\bigr)$$ with a real potential $q\in L^1(\mathbb R)$ covers the whole real line and, in addition, non-real eigenvalues may appear if the potential $q$ assumes negative values. A quantitative analysis of the non-real eigenvalues is a challenging problem, and so far only partial results in this direction were obtained. In this paper the bound $$|\lambda|\leq |q|_{L^1}^2$$ on the absolute values of the non-real eigenvalues $\lambda$ of $A$ is obtained. Furthermore, separate bounds on the imaginary parts and absolute values of these eigenvalues are proved in terms of the $L^1$-norm of the negative part of $q$.Comment: to appear in Proc. Amer. Math. So

The spectra of indefinite singular Sturm-Liouville operators

In der vorliegenden Arbeit werden die spektralen Eigenschaften singulärer Sturm-Liouville- Differentialoperatoren der Form Af=1/r(︁−(pf′)′ + qf)︁ mit reellwertigen Koeffizienten p, q und r untersucht. Hierbei betrachten wir indefinite Gewichtsfunktionen r. Basierend auf Erkenntnissen der relativen Oszillationstheorie sowie der Floquet-Theorie für periodische Sturm-Liouville-Operatoren werden Kriterien nachgewiesen, welche die Stabilität der essentiellen Spektren unter Störung der Koeffizienten sicherstellen. Außerdem wird die Häufung von Eigenwerten in den Lücken des essentiellen Spektrums untersucht. Wir formulieren Bedingungen, die eine Häufung der Eigenwerte innerhalb einer Lücke implizieren, bzw. eine Häufung ausschließen. Weiterhin werden die nichtreellen Spektren indefiniter Sturm-Liouville-Operatoren untersucht. Hierbei werden Schranken der nichtreellen Eigenwerte hinsichtlich ihres Absolutbetrages and Imaginärteils bestimmt. Der Nachweis der Schranken beruht auf einer gewissenhaften Analyse der zugehörigen Eigenfunktionen.In this thesis we study the spectral properties of singular Sturm–Liouville differential operators of the form Af=1/r(︁−(pf′)′ + qf)︁ with real-valued coefficients p, q and r, where the weight function r is indefinite. We present criteria guaranteeing the stability of the essential spectrum under perturbation with respect to the coefficients. Further, the accumulation of eigenvalues within gaps of the essential spectrum is studied. We show criteria which imply the finiteness or the accumulation of the point spectrum within a gap of the essential spectrum. The results are based on relative oscillation theory and the Floquet theory for periodic Sturm–Liouville problems. Moreover, we focus on the non-real spectra of indefinite Sturm–Liouville operators. We establish bounds on the absolute values and imaginary parts of the non-real eigenvalues. The verification of these bounds bases on a careful analysis of the corresponding eigenfunctions

Individual Investor Sentiment and Stock Returns - What Do We Learn from Warrant Traders?

In this paper, we propose a measure of individual investor sentiment that is derived from the market for bank-issued warrants. Due to a unique warrant transaction data set from a large discount broker we are able to calculate a daily sentiment measure and test whether individual investor sentiment is related to daily stock returns by using vector autoregressive models and Granger causality tests. We find that there exists a mutual influence of sentiment and stock market returns, but only in the very short-run (one and two trading days). Returns have a negative influence on sentiment, while the influence of sentiment on returns is positive for the next trading day. The influence of stock market returns on sentiment is stronger than vice versa. Our sentiment measure simultaneously avoids problems that are associated with existing sentiment measures, which are based on the closed-end fund discount, stock market transactions, the put-call ratio or investor surveys.

Privatanleger am Optionsscheinmarkt

Trotz der enormen Bedeutung, die Optionsscheine in den letzten Jahren erlangt haben, gibt es bisher in der wissenschaftlichen Literatur kaum Erkenntnisse über die Akteure, die in diesem Markt aktiv sind und deren Transaktionsverhalten. Die vorliegende Arbeit will diese Lücke schließen. Wir stellen einerseits umfassend den Markt für Optionsscheine in Deutschland dar. Andererseits analysieren wir das tatsächliche Verhalten von ca. 1.500 Privatanlegern eines deutschen Online-Brokers und stellen eine Vielzahl von stilisierten Fakten dar. Wir ermitteln beispielsweise, dass Optionscheinhändler jünger sind als reine Aktienmarktinvestoren und dass sie eine in vielen Facetten riskantere und kurzfristiger orientierte Anlagestrategie verfolgen. Außerdem ist das Transaktionsverhalten unterschiedlich, wenn den Optionsscheinen statt einzelnen Aktien ganze Aktienindizes oder andere Basiswerte zugrunde liegen. Des Weiteren zeigen wir, dass die Optionsscheine nur sehr kurze Zeit in den Portfolios der Privatanleger verbleiben und dass das Absicherungsmotiv bei der Anlage in Verkausoptionsscheine bestenfalls eine untergeordnete Rolle spielt. Zusätzlich kann erstmals der Erfolg der Privatanleger am Optionsscheinmarkt dargestellt werden. Im Durchschnitt erzielten die Anleger eine positive (nicht risikoadjustierte) Rendite, die aber einzig auf Transaktionen mit Kaufoptionsscheinen auf Einzelaktien während der Hausse bis März 2000 zurückzuführen war. Darüber hinaus können wir für Aktieninvestoren umfassend bestätigte Phänomene wie den Dispositionseffekt auch für Optionsscheinhändler nachweisen. Der Privatanlegerdatensatz umfasst über 100.000 Transaktionen in mehr als 8.000 Optionsscheinen und lässt damit einen bisher einmaligen Einblick in das Handelsverhalten von Anlegern in dieser Wertpapierkategorie zu

Buying and Selling Behavior of Individual Investors in Option-like Securities

We analyze the trading behavior of individual investors in option-like securities, namely bank-issued warrants, and thus expand the growing literature of investors behavior to a new kind of securities. A unique data set from a large German discount broker gives us the opportunity to analyze the trading behavior of 1,454 investors, making 89,958 transactions in 6,724 warrants on 397 underlyings. In different logit regression, we make use of the facts that investors can speculate on rising and falling prices of the underlying with call and put warrants and that we also have information about the stock portfolios of the investors. We report several facts about the trading behavior of individual investors in warrants that are consistent with the literature on the behavior of individual investors in the stock market. The warrant investors buy calls and sell puts if the price of the underlying has decreased over the past trading days and they sell calls and buy puts if the price of the underlying has increased. That means, the investors follow negative feedback trading strategies in all four trading categories observed. In addition, we find strong evidence for the disposition effect for call as well as put warrants. The trading behavior is also influenced if the underlying reaches some exceptionally prices, e.g. highs, lows or the strike price. We show that hedging, as one natural candidate to buy puts, does not play an important role in the market for bank-issued warrants. The probability to buy calls is positively related to the holding of the underlying in the portfolio, meaning that investors tend to leverage their stock positions, while the relation between put purchases and portfolio holdings of the underlying is negative. Differences in the trading behavior in warrants with stock market indexes or single stocks as underlings are small

Tax compliance and information provision - A field experiment with small firms

We study tax compliance in Slovenia using data generated in a field experiment. Small accounting companies were randomly assigned to an untreated control group and two treatment groups. Companies in the first treatment group received a letter that highlighted the importance of paying taxes and informed about the likelihood of becoming subject to an audit. In the second treatment group, tax officers from the tax authorities handed out in person the same letter that companies in the first treatment group received by post. The results indicate that such letters can increase compliance, and trigger even more compliance if handed over in person. These findings are in line with the theoretical predictions that we derive to rationalize the experiment

Investigation of the Dynamic Heat Transfer Coefficient of R-134a in a Horizontal Pipe

The German automotive industry is trying to achieve full electric mobility in Germany. Therefore the research focus is on the battery as the new primary energy storage. Not only the shorter range and higher costs of this technology are a problem. In addition to that, the battery is a highly dynamic and demanding consumer from a thermodynamic point of view. The working temperature is limited to the range between 20 and 40 °C. Below 0 °C and over 60 °C the life expectancy and the capacity would take damage. Thus the air conditioning cycle of the automobile needs to be adapted to the new challenge. Since the industry wants to simulate every state of the dynamic air conditioning system in the car, numerically robust models are required. A dynamic system model was created and tested in Modelica. Experience shows that in particular low heat loads and mass flows close to zero are causing problems to the solvability of such dynamic cooling cycles. One aspect of these numerical problems is the dynamic heat transfer coefficient at these marginal loads. Hence the aim of the study at the Institute of Thermo-Fluid Dynamics is to investigate the dynamic behavior of the heat transfer coefficient under these conditions for the refrigerant R-134a. This paper presents a test rig to measure the heat transfer coefficient of the refrigerant R-134a in a small diameter horizontal pipe. The experiment layout is basically a cooling cycle. The basic components are a receiver tank filled with R-134a, a pump, an evaporator pipe and a condenser. The evaporator pipe made out of copper is the main element. Thermocouples, pressure sensors and a mass flow sensor provide the information necessary to determine the heat transfer coefficient of the horizontal pipe. In addition to the cycle the natural convection of R-134a in the pipe is of interest. Because there are working points of the automobile, where a small heat load is applied and the air conditioning is switched off. Besides the experimental investigations a FEM model is build. With COMSOL Multiphysics the two-phase-flow is simulated and compared with the results of the experiments. The Validation is an important step to build a numerically robust model for the system simulation with Modelica

Individual Investor Sentiment and Stock Returns - What Do We Learn from Warrant Traders?

In this paper, we propose a measure of individual investor sentiment that is derived from the market for bank-issued warrants. Due to a unique warrant transaction data set from a large discount broker we are able to calculate a daily sentiment measure and test whether individual investor sentiment is related to daily stock returns by using vector autoregressive models and Granger causality tests. Our sentiment measure should be, ex ante, the preferred measure when compared to other sentiment measures proposed in the literature that are based on the closed-end fund discount, stock market transactions, the put-call ratio or investor surveys as it circumvents problems that are associated with the measures used in prior studies. We find that there exists a mutual influence between sentiment and stock market returns, but only in the very short-run (one and two trading days). Returns have a negative influence on sentiment, while the influence of sentiment on returns is positive for the next trading day. The influence of stock market returns on sentiment is stronger than vice versa. Our results cast doubt on whether sentiment measures are useful to predict the market over horizons of more than one day. Even our improved measure is hardly able to do so. Nevertheless, sentiment measures provide evidence on how investors trade and which factors influence their expectations

PT-Symmetric Hamiltonians as couplings of dual pairs

In the seminal paper (Bender & Boettcher, 1998) a new view of quantum mechanics was proposed. This new view differs from the old one in that the restriction on the Hamiltonian to be Hermitian is relaxed: now the Hamiltonian is PT -symmetric. Here P is parity and T is time reversal. Since 1998, PT -symmetric Hamiltonians have been analyzed intensively by many authors. In Mostafazadeh (2002) PT -symmetry was embedded into the more general mathematical framework of pseudo-Hermiticity or, what is the same, self-adjoint operators in Kre˘ın spaces, see (Langer & Tretter, 2004; Azizov & Trunk, 2012; Hassi & Kuzhel, 2013; Leben & Trunk, 2019). For a general introduction to PT -symmetric quantum mechanics we refer to the overview paper of Mostafazadeh (2010) and to the books of Moiseyev (2011) and Bender (2019)