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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.