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The aim of this article is to establish a stochastic search algorithm for neural networks based on the fractional stochastic processes {đ”đ»đĄ,đĄâ„0} with the Hurst parameter đ»â(0,1). We define and discuss the properties of fractional stochastic processes, {đ”đ»đĄ,đĄâ„0}, which generalize a standard Brownian motion. Fractional stochastic processes capture useful yet different properties in order to simulate real-world phenomena. This approach provides new insights to stochastic gradient descent (SGD) algorithms in machine learning. We exhibit convergence properties for fractional stochastic processes.
The aim of this work is to establish and generalize a relationship between fractional partial differential equations (fPDEs) and stochastic differential equations (SDEs) to a wider class of stochastic processes, including fractional Brownian motions and sub-fractional Brownian motions with Hurst parameter H â (1/2,1). We start by establishing the connection between a fPDE and SDE via the Feynman-Kac Theorem, which provides a stochastic representation of a general Cauchy problem. In hindsight, we extend this connection by assuming SDEs with fractional and sub-fractional Brownian motions and prove the generalized Feynman-Kac formulas under a (sub-)fractional Brownian motion. An application of the theorem demonstrates, as a by-product, the solution of a fractional integral, which has relevance in probability theory.
Die Debatte ĂŒber die Zukunft der EuropĂ€ischen Wirtschafts- und WĂ€hrungsunion ist seit geraumer Zeit omniprĂ€sent (Herzog und Hengstermann 2013). Mit der temporĂ€ren Aussetzung der europĂ€ischen (nationalen) Schuldenregeln bis zum 31. Dezember 2022 ging abermals eine leidenschaftlich gefĂŒhrte Post-Covid-19-Reformdiskussion los. Zu den bisherigen VerĂ€nderungsnotwendigkeiten kommen nunmehr die geopolitischen Herausforderungen hinzu. Ist die StabilitĂ€t der WĂ€hrungsunion in Gefahr?
Rational behavior is a standard assumption in science. Indeed, rationality is required for environmental action towards net-zero emissions or public health interventions during the SARS-CoV-2 pandemic. Yet, little is known about the elements of rationality. This paper explores a dualism of rationality comprised of optimality and consistency. By designing a new guessing game, we experimentally uncover and disentangle two building blocks of human rationality: the notions of optimality and consistency. We find evidence that rationality is largely associated to optimality and weakly to consistency. Remarkably, under uncertainty, rationality gradually shifts to a heuristic notion. Our findings provide insights to better understand human decision making.
This article explores the determinants of peopleâs growth prospects in survey data as well as the impact of the European recovery fund to future growth. The focus is on the aftermath of the Corona pandemic, which is a natural limit to the sample size. We use Eurobarometer survey data and macroeconomic variables, such as GDP, unemployment, public deficit, inflation, bond yields, and fiscal spending data. We estimate a variety of panel regression models and develop a new simulation-regression methodology due to limitation of the sample size. We find the major determinant of peopleâs growth prospect is domestic GDP per capita, while European fiscal aid does not significantly matter. In addition, we exhibit with the simulation-regression method novel scientific insights, significant outcomes, and a policy conclusion alike.
This article studies the effects of reverse factoring in a supply chain when the buyer company facilitates its lower short-term borrowing rates to the supplier corporation in return for extended payment terms. We explore the role of interest rate changes, rating changes, and the business cycle position on the cost and benefit trade-off from a supplier perspective. We utilize a combined empirical approach consisting of an event study in Step 1 and a simulation model in Step 2. The event study identifies the quantitative magnitude of central bank decisions and rating changes on the interest rate differential. The simulation computes with a rolling-window methodology the daily cost and benefits of reverse factoring from 2010 to 2018 under the assumption of the efficient market hypothesis. Our major finding is that changes of crucial financial variables such as interest rates, ratings, or news alerts will turn former win-win into win-lose situations for the supplier contingent to the business cycle. Overall, our results exhibit sophisticated trade-offs under reverse factoring and consequently require a careful evaluation in managerial decisions.
This paper studies the power of online search intensity metrics, measured by Google, for examining and forecasting exchange rates. We use panel data consisting of quarterly time series from 2004 to 2018 and ten international countries with the highest currency trading volume. Newly, we include various Google search intensity metrics to our panel data. We find that online search improves the overall econometric models and fits. First, four out of ten search variables are robustly significant at one percent and enhance the macroeconomic exchange rate models. Second, country regressions corroborate the panel results, yet the predictive power of search intensity with regard to exchange rates vary by country. Third, we find higher prediction performance for our exchange rate models with search intensity, particularly in regard to the direction of the exchange rate. Overall, our approach reveals a value-added of search intensity in exchange rate models.
In this paper, we examine the political gridlock in reforming the Economic and Monetary Union. We utilize a twoâstage game with imperfect information in order to study the optimal sequencing. The main results are: first, optimal sequencing requires for incompliant Member States a default option in stageâtwo, which in principle is related to the today's fiscal architecture (EMU-I). Second, we show that compliant countries prefer a reform equilibrium today if and only if they have a free choice about the preferred fiscal architecture at the end â either EMU-II with binding European coordination or EMU-I related to Maastricht. Noteworthy, our sequencing approach works for any design of the EMU-II architecture.
Das Weltwirtschaftswachstum der vergangenen Jahrzehnte war durch die Dynamik der Digitalisierung und Globalisierung in den Lieferketten geprĂ€gt. Die Corona-Pandemie hat die AbhĂ€ngigkeit und Verletzlichkeit der Lieferketten offengelegt. Trotz einer Vielzahl verbindlicher Standards haben Unternehmen die Digitalisierung und Arbeitsteilung auch fĂŒr regulatorische Arbitrage genutzt. Einerseits erhöht das die Effizienz der Wirtschaft - was mithin ökologische Ressourcen schont - andererseits werden damit internationale Standards konterkariert. Globalisierung und Digitalisierung sind Segen und Fluch zugleich.
This article studies the hidden blemishes of two benchmark rulings of the European Court of Justice (ECJ). In 2015 and 2018, the ECJ approved two unconventional monetary instruments, among others âOutright Monetary Transactionsâ and the âPublic Sector Purchase Programâ. Yet, there is a vigorous debate about both monetary operations in law and economics. In this interdisciplinary article, we address law and economic arguments in order to elucidate insights to the legal community. In particular, we elaborate on the legal implications of a variety of concerning issues such as public policy interference, effect on wealth redistribution, erosion of democratic legitimacy and lack of effectiveness of monetary policy. These topics remain disregarded in the ECJ rulings. Consequently, the verdicts do not identify the economic boundaries of the European Central Bankâs mandate appropriately.
This article studies the renewed interest surrounding sustainable public finance and the topic of tax evasion as well as the new theory of information inattention. Extending a model of tax evasion with the notion of inattention reveals novel findings about policy instruments that can be used to mitigate tax evasion. We show that the attention parameters regarding tax rates, financial penalty schemes and income levels are as important as the level of the detection probability and the financial penalty incurred. Thus, our theory recommends the enhancement of sustainability in public policy, particularly in tax policy. Consequently, the paper contributes both to the academic and public policy debate.
This paper studies the impact of financial liquidity on the macro-economy. We extend a classic macroeconomic modeland compute numerical simulations. The model confirms that persistently low inflation can occur despite a high degreeof financial liquidity due to a reallocation of cash, normal and risk-free bonds. In that regard, our model uncovers anexplanation of a flat Phillips curve. Overall, our approach contributes to a rather disregarded matter in macroeconomictheory.
Das Urteil des Bundesverfassungsgerichts (BVerfG) vom 5. Mai 2020 ist Schlusspunkt und zugleich Neuanfang nach einer jahrelangen verfassungsrechtlichen und ökonomischen Auseinandersetzung. Im Prinzip geht es um die konstituierenden Prinzipien der Eurozone sowie das Mandat der EuropĂ€ischen Zentralbank (EZB). Der EU-Vertrag charakterisiert die Leitplanken der Wirtschafts- und WĂ€hrungsunion (WWU) im Spannungsfeld der Art. 119, 123 und 125 des Vertrags ĂŒber die Arbeitsweise der EuropĂ€ischen Union (AEUV). Mithin liegt die wirtschaftspolitische SouverĂ€nitĂ€t â nach dem Prinzip Haftung und Kontrolle â allein bei den Mitgliedstaaten. Die Organe der EuropĂ€ischen Union (EU) sowie der Gerichtshof der EuropĂ€ischen Union (EuGH) legen diese Leitplanken gemÀà dem Leitgedanken in Art. 1 des Vertrags ĂŒber die EuropĂ€ische Union (EUV) einer âever closer unionâ regelmĂ€Ăig mit weitem Ermessen aus.
This article studies the current debate on Coronabonds and the idea of European public debt in the aftermath of the Corona pandemic. According to the EU-Treaty economic and fiscal policy remains in the sovereignty of Member States. Therefore, joint European debt instruments are risky and trigger moral hazard and free-riding in the Eurozone. We exhibit that a mixture of the principle of liability and control impairs the present fiscal architecture and destabilizes the Eurozone. We recommend that Member States ought to utilize either the existing fiscal architecture available or establish a political union with full sovereignty in Europe. This policy conclusion is supported by the PSPP-judgement of the Federal Constitutional Court of Germany on 5 May 2020. This ruling initiated a lively debate about the future of the Eurozone and Europe in general.
Since 2000, Indian special economic zones were established with the intention to attract foreign direct investment. We present a first empirical assessment with new data from 1980 to 2010 and evaluate the outcome after 10 years. In general, our empirical results confirm that special economic zones attract FDI statistical significantly. Another finding of the study is that open economies with stable inflation attract more FDI than small and closed economies.
Disziplinierung ohne politische Diskriminierung: warum es MarktkrÀfte in der WÀhrungsunion bedarf!
(2019)
Die Reform der WĂ€hrungsunion sollte folgende zwei Aspekte verknĂŒpfen: einerseits die Ăbernahme einer stĂ€rkeren politischen StabilitĂ€tsverantwortung und andererseits die StĂ€rkung der MarktkrĂ€fte. Nur so kann das Prinzip von Eigenverantwortung und Haftung abgesichert werden. Zudem sollte die Politik im Euroraum einen Abwicklungsmechanismus fĂŒr ĂŒberschuldete MitgliedslĂ€nder etablieren.
This paper studies option pricing based on a reverse engineering (RE) approach. We utilize artificial intelligence in order to numerically compute the prices of options. The data consist of more than 5000 call- and put-options from the German stock market. First, we find that option pricing under reverse engineering obtains a smaller root mean square error to market prices. Second, we show that the reverse engineering model is reliant on training data. In general, the novel idea of reverse engineering is a rewarding direction for future research. It circumvents the limitations of finance theory, among others strong assumptions and numerical approximations under the BlackâScholes model.
Nach der Euro- und Wirtschaftskrise in den Jahren seit 2010 verzeichnet die EuropĂ€ische Union (EU) derzeit einen soliden Wirtschaftsaufschwung in allen Mitgliedstaaten. Der Anteil Europas an der Weltwirtschaft betrĂ€gt rund 30 Prozent. Das europĂ€ische Wirtschaftswachstum ist 2018 mit 2,1 Prozent sogar gröĂer als das in Deutschland mit 1,6 Prozent. Eine Analyse der Dauer von Aufschwungsphasen zeigt, dass Europa im Vergleich zur Weltwirtschaft sogar unerwarteter Spitzenreiter ist. Seit den 1970er-Jahren liegt die durchschnittliche Dauer eines europĂ€ischen Wirtschaftsaufschwungs bei ĂŒber dreiĂig Quartalen; sie ist mithin deutlich höher als in den USA und Japan.
This paper develops a new methodology in order to study the role of dynamic expectations. Neither reference-point theories nor feedback models are sufficient to describe human expectations in a dynamic market environment. We use an interdisciplinary approach and demonstrate that expectations of non-learning agents are time-invariant and isotropic. On the contrary, learning enhances expectations. We uncover the âyardstick of expectationsâ in order to assess the impact of market developments on expectations. For the first time in the literature, we reveal new insights about the motion of dynamic expectations. Finally, the model is suitable for an AI approach and has major implications on the behaviour of market participants.