Stability of functional equations connected with quadrature rules

We study the stability properties of the equation F(y)−F(x)=(y−x)∑i=1naif(αix+βiy) which is motivated by numerical integration. In Szostok and Wa̧sowicz (Appl Math Lett 24(4):541–544, 2011) the stability of the simplest equation of the type (0.1) was investigated thus the inequality |F(y)−F(x)−(y−x)f(x+y)|≤ε was studied. In the current paper we present a somewhat different approach to the problem of stability of (0.1). Namely, we deal with the inequality ∣∣∣F(y)−F(x)y−x−∑i=1naif(αix+βiy)∣∣∣≤ε

Banks' Performance over the Business Cycle: A Panel Analysis on Italian Intermediaries

Supervisors and policy makers pay increasing attention to the possible procyclical nature of banks’ behaviour. Indeed, to guarantee macro and financial stability, it is important to understand if, and to what extent, banks are affected by the macroeconomy and if there are second round effects. This paper provides a comprehensive investigation on these issues using a large dataset of Italian intermediaries over the period 1985-2002. In particular, estimating both static and dynamic models, it investigates whether loan loss provisions, nonperforming loans and the return on assets show a cyclical pattern. The estimated relations are then employed to carry out simple stress tests aiming at assessing the effects of macroeconomic shocks on banks’ balance sheets.banking supervision; loan loss provisions; non-performing loans; procyclicality; stress test

A higher order model for thin-walled structures with deformable cross-sections

AbstractA higher order model for the analysis of linear, prismatic thin-walled structures that considers the cross-section warping together with the cross-section in-plane flexural deformation is presented in this paper. The use of a one-dimentional model for the analysis of thin-walled structures, which have an inherent complex three-dimensional (3D) behaviour, can only be successful and competitive when compared with shell finite element models if it fulfills a twofold objective: (i) an enrichment of the model in order to as accurately as possible reproduce its 3D elasticity equations and (ii) the definition of a consistent criterion for uncoupling the beam equations, allowing to identify structural deformation modes.The displacement field is approximated through a linear combination of products between a set of linear independent functions defined over the cross-section and the associated weights only dependent on the beam axis; this approximation is not constrained by any ab initio kinematic assumptions. Towards an efficient application of the approximation procedure, the cross-section is discretized into thin-walled elements, being the displacement field approximated for each element independently of the displacement direction. The approximation is thus hp refined enhancing the “capture” of the 3D structural mechanics of thin-walled structures. The beam model governing equations are obtained through the integration over the cross-section of the corresponding elasticity equations weighted by the cross-section global approximation functions.A criterion for uncoupling the beam governing equations is established, allowing to (i) retrieve the classic equations of the thin-walled beam theory both for open and closed sections and (ii) derive a set of uncoupled deformation modes representing higher order effects. The criterion is based on the solution of the polynomial eigenvalue problem associated with the beam differential equations, allowing to quantify the Saint-Venant principle for thin-walled structures. In fact, the solution of the non linear eigenvalue problem yields a twelve fold null eigenvalue (representing polynomial solutions) that are verified to represent beam classic solutions and sets of pairs and quadruplets of non-null eigenvalues corresponding to higher order modes of deformation

Essays on Non-linearities in Macroeconomics

This dissertation consists of three essays studying different topics in macroeconomics under the common aim of assessing the role of nonlinear dynamics in explaining selected facts of interest. In Chapter 1, co-authored with Marzio Bassanin and Ester Faia, we explore the linkages between financial crises and debt markets, where collateral constraints and opacity of asset values are the norm. We, therefore, introduce ambiguity attitudes in beliefs formation in a small open economy model where borrowers investing in risky assets face occasionally binding collateral constraints. We estimate the ambiguity attitudes process and derive that borrowers endogenously act optimistically in booms and pessimistically in recessions. Analytically and numerically we show that our ambiguity attitudes coupled with the collateral constraints crucially help explaining asset price and debt cycle facts. Chapter 2 studies the pass-through of sovereign risk in an environment where latent condence factors, along with fundamentals, might feed debt crises. A Markov-switching VAR with three variables (private spread, sovereign spread, debt-to-GDP) is estimated on fiscally-leveraged economies (Italy, Spain, Portugal). By allowing fiscal and financial sources of amplication, the model historically identies: i ) an high vulnerability regime, where sovereign spreads show excessive sensitiveness to fiscal imbalances. Those periods line up mostly with the global financial turmoil and the sovereign European debt crisis; ii ) an high synchronization regime where the sovereign and financial risk measures are strongly tied in a synchronized comovement. Those period identify more the first phases of the two crises. Finally, Chapter 3, co-authored with Othman Bouabdallah and Pascal Jacquinot, aims to extract an empirical narrative for France on the relationship between fiscal policy and debt sustainability, in the context of fiscal regimes. We build a DSGE model, where Markov-switching dynamics are introduced on the tax revenues response to debt, expenditure and output gap. We then bring the model to the data and show that two distinct fiscal regimes took place over the period 1955-2009: a sustainable regime covered `Les Trente Glorieuses' until 1977 and then re-emerged in 1999 with the euro membership; an unsustainable regime, instead, characterised the 1978-1998 period, where a policy mix of disinflation, external and internal balance led to primary deits and unstable debt-to-GDP accumulation

Microstructural-Based Modeling Framework for High Temperature Behavior of Ferritic-Martensitic Steels Using Crystal Plasticity and Grain Boundary Finite Element Approaches

Ferritic/martensitic 9-12Cr steel alloys, have had widespread use as structural materials in power plants. Among this family of alloys, Grade 91 (Gr91) steel was a landmark in the development of 9-12Cr alloys. However, the unique microstructure complexity of the alloy has raised doubt regarding the techniques of data extrapolation in estimating its service-life for operation in next-generation power plants at higher temperatures and presssures. Conservatism becomes essential when the alloy is to be used in components lasting the life-cycle of power plants without replacement.This dissertation develops a physically-based microstructural model for creep rupture at 600 degrees Celsius for Gr91 steel as well as fundamental modeling tools that apply more broadly to microstructural modeling in metals. Key features of the Gr91 modeling framework capture the mechanical behavior of its prior austenite grains (PAG) and grain boundaries. Ultimately, a constitutive expression was adopted that captured the response from experiments conducted in the creep strain rate regime.An initial model intended to simulate low-cycle fatigue was first developed using the idea of geometrically necessary dislocations (GNDs) in crystal plasticity (CP) framework. That necessitated evaluating strain gradients and a patch-recovery method was implemented to recover a linear elastic deformation gradient field across the domain in linear elements. A Lie-group to Lie-algebra mapping was used to preserve orthogonality when projecting the rotation tensor from the elements’ Gauss points to the nodes.A statistically-stored dislocation density model was investigated to span the regimes of moderate strain rates (tension tests) to low strain rates (creep tests). Calibration of this model was possible against tension tests, but its application to creept tests suggested that other dislocation mechanisms were present during the primary creep regime of Gr91. Therefore, the CP model in the PAGs was changed to represent dislocation climb-glide motion and recovery along with linear viscous diffusional creep for point defect diffusion. This revised model more closely captured the measurements of creep response.Lastly, a robust Discontinuous Galerkin method is proposed to model the grain boundary interface elements to address traction oscillations observed for cohesive models. Stability and convergence are assessed along with non-conforming meshes

Darstellbare Optionen

We call a given American option representable if there exists a European claim which dominates the American payoff function at any time and such that the values of the two options coincide within the continuation set associated to the American option. This mathematical concept has interesting implications from a probabilistic, analytic,financial and numerical point of view. We aim at analyzing the notion of representability and linking it to embedded American payoffs in the sense of Jourdain and Martini (2001) and cheapest dominating European options originating from the work of Christensen (2014).This process reveals a new duality structure between European and American valuation problems which we deem as very promising for future research. Relying on methods from convex optimization, we make a first step towards verifying representability of certain American claims. Furthermore, we discuss some computational aspects related to semi-infinite linear programming theory. This ultimately leads to an iterative procedure which generates upper and lower bounds for American option prices as well as a spline approximation to the early exercise boundary. The algorithm is benchmarked against high-precision methods from the literature.Wir bezeichnen ein amerikanisches Derivat als darstellbar, falls eine europäische Option existiert, welche innerhalb des Fortsetzungsgebietes preisgleich zu der amerikanischen Option ist und deren assoziierte Wertfunktion den amerikanischen Payoff zu jeder Zeit dominiert. Aus diesem Konzept lassen sich diverse Schlüsse ableiten, welche sowohl aus einer wahrscheinlichkeitstheoretischen oder finanzmathematischen Perspektive, als auch von einem analytischen oder numerischen Standpunkt aus betrachtet von Interesse sind. Die vorliegende Dissertation zielt darauf ab, mittels Darstellbarkeit eine Brücke zwischen eingebetteten amerikanischen Auszahlungen, im Sinne von Jourdain und Martini (2001), und den von Christensen (2014) diskutierten billigst dominierenden europäischen Optionen, zu schlagen. Hierbei stoßen wir auf einen bisher unbekannten strukturellen Zusammenhang zwischen amerikanischer und europäischer Optionsbewertung. Diesen erachten wir als interessant und reichhaltig hinsichtlich zukünftiger Forschungsvorhaben. Für gewisse amerikanische Auszahlungsprofile wagen wir, unter Zuhilfenahme von Methoden der konvexen Optimierung, einen ersten Schritt in Richtung Lösung des Darstellbarkeitsproblems. Ergänzend diskutieren wir einige algorithmische Aspekte im Rahmen der Theorie semi-infiniter linearer Programme. Abschließend präsentieren wir ein iteratives Verfahren, welches sowohl obere und untere Schranken für amerikanische Optionspreise, als auch eine Spline Approximation der Ausübungsgrenze generiert. Zur Leistungsbemessung ziehen wir Präzisionsmethoden aus der Fachliteratur zu Rate

A macroscopic plasma Lagrangian and its application to wave interactions and resonances

The derivation of a macroscopic plasma Lagrangian is considered, along with its application to the description of nonlinear three-wave interaction in a homogeneous plasma and linear resonance oscillations in a inhomogeneous plasma. One approach to obtain the Lagrangian is via the inverse problem of the calculus of variations for arbitrary first and second order quasilinear partial differential systems. Necessary and sufficient conditions for the given equations to be Euler-Lagrange equations of a Lagrangian are obtained. These conditions are then used to determine the transformations that convert some classes of non-Euler-Lagrange equations to Euler-Lagrange equation form. The Lagrangians for a linear resistive transmission line and a linear warm collisional plasma are derived as examples. Using energy considerations, the correct macroscopic plasma Lagrangian is shown to differ from the velocity-integrated low Lagrangian by a macroscopic potential energy that equals twice the particle thermal kinetic energy plus the energy lost by heat conduction

Skills substitution and trust: a new conception of attitude towards AI in a-HRM

Attitude towards new technologies depends on different factors. In case of AI (artificial intelligence), workers may perceive their own skills as easily substitutable and look at their job as likely to be replaced. This perception may have negative impact on their acceptance towards implementation of intelligent machines and automation, if there wouldn’t be a well based trust on the improvements brought by these technologies. Unfolding from such considerations, we have collected data from a diversified sample of 183 workers and requested a bootstrapped estimate from 5,000 samples. As a result, we propose a mediated process between skills substitution and perceived overall job replacement, moderated by trust, which leads to attitude towards AI in a-HRM (automated human resources management). Surprisingly for high substitution perceptions, workers manifested more positive attitude towards AI. This provided big room of discussion and great enrichments in current literature; plus considerable practical implication in understanding workers behaviors face automation investments in companies.A atitude em relação às novas tecnologias depende de diferentes fatores. No caso da IA (inteligência artificial), os trabalhadores podem perceber as próprias competências como facilmente substituíveis e perceber a instabilidade do seu trabalho. Essa perceção pode ter um impacto negativo na aceitação da implementação de máquinas inteligentes e de investimentos em automação, se não houvesse uma confiança bem fundamentada nas melhorias trazidas por essas tecnologias. Começando de tais considerações, coletamos dados de uma amostra diversificada de 183 trabalhadores e solicitamos uma bootstrapped estimate de 5.000 amostras. Como resultado, propomos um modelo mediado entre a substituição de competências e a perceção geral da substituição do trabalho, moderada pela confiança, o que leva a atitude face as IA em a-HRM (automated human resources management). Surpreendentemente, para perceções de alta substituição, os trabalhadores manifestaram uma atitude mais positiva em relação as IA. Isso proporcionou grande espaço de discussão e grandes enriquecimentos na literatura atual, mais implicações práticas fundamentais na compreensão dos comportamentos dos trabalhadores em frente aos investimentos em automação nas empresas

A variational multiscale computational framework for reaction-dominated thermo-chemo-mechanical process modeling in multi-constituent material systems

This dissertation develops a computational framework for modeling multi-constituent material systems characterized by the transport of reacting fluids through deformable solids, and their coupled, nonlinear, thermo-chemo-mechanical response in the reaction-dominated regime. This is accomplished through two major components of the work: (i) new robust variational multi-scale numerical methods that are consistently derived, and (ii) models for multi-physics processes in multi-constituent materials. New robust numerical methods are developed via the variational multiscale (VMS) framework. Through the concept of fine scales in VMS, unresolved physics are recovered and embedded at the coarse scale level, improving stability and accuracy of the method. Focus is placed on fine scales that do not vanish at element boundaries (so-called “edge bubbles”). Using edge bubbles and an explicit time integration algorithm, a VMS Discontinuous Galerkin (VMDG) method is derived for multi-domain problems in elastodynamics where different subdomains can be solved synchronously and concurrently with minimal sharing of information. In addition, a new VMS method is introduced for the reaction-dominated regime of the diffusion–reaction equation. The proposed fine-scale basis consists of enrichment functions that may be nonzero at element edges. The method captures sharp boundary and internal layers, suppresses spurious oscillations, and better satisfies the maximum principle as compared to other existing methods. A priori mathematical analysis of the stability and convergence of the method is presented, and optimal rates of convergence are verified numerically. The numerical methods developed in this work may be applied to many reaction-diffusion systems in mathematical models for coupled thermo-chemo-mechanical phenomena arising from different theoretical frameworks. Here, a model for thermo-chemo-mechanical response of open solid-fluid systems is presented in the context of mixture theory. Derivation starts from constituent-wise equations for balance of mass, momentum, and energy, accounting for energy in formation and breaking of chemical bonds. Interactions between different constituents are captured through interaction terms as per locally homogenized mixture theory. Satisfaction of the second law of thermodynamics is achieved by providing constitutive equations that guarantee non-negative entropy production. Resulting mathematical models yield transient diffusion-advection-reaction problems posed by systems of coupled, nonlinear, second-order partial differential equations (PDEs), whose solution require stable numerical methods. Several numerical studies are presented to highlight stability, accuracy, and other features of the newly developed variational multiscale methods and thermo-chemo-mechanical models. Tests involve hypothetical as well as realistic materials with boundary layers, advancing reaction fronts, chemical swelling, and fingering phenomena

Some theoretical aspects of econometric inference with heteroskedastic models

This Thesis is concerned with econometric inference in parametric heteroskedastic models. Each moment of the conditional distribution can be seen as a source of information which provides an estimating equation for the parameter vector. Different issues arise in the different moments concerning the identifiability of parameters, the observability of the dependent variable of the estimating equation, and the positivity restrictions implicit in even order moments. Estimators of the identifiable functions of the parameter vector are obtained from orthogonality conditions in each moment. Under symmetry of the distribution, the sources of information corresponding to the first two conditional moments are independent, at least asymptotically, and the information about common parameters is combined in estimation by constructing a matrix weighted average. Estimation procedures under normality are viewed in a maximum likelihood framework, and generalized method of moments estimation provides the setup for the analysis of more general distributions. The separation of the information into its moment source constitutes a basic element for diagnostic testing of the model. The implications of different forms of misspecification are analyzed and robustness properties are established for some leading cases, especially the ARCH class of models. A general framework is presented for diagnostic testing of heteroskedastic models, which includes tests of the coherency of the information contributed by the two moments, a family of 'consistency tests' which concentrates on the assessment of the first two moments, and a family of 'efficiency tests' which concentrates on checking the specification of moments of order three and higher. The consistency and efficiency tests may be constructed without using information external to the model and thus may be reported with standard computer output, but these families also include many LM tests against specific departures by suitable choice of the test parameters. Tests for autocorrelation, dynamics, parameter stability, different types of exogeneity, and normality, are analyzed in particular. The estimation and diagnostic testing framework is extended to the inclusion of la ten t variables in the conditional mean, such as parametric risk measures and varying coefficients, and also to a multivariate setting. Finally, the problem of extracting information from higher order moments is considered by looking a t the information th a t each moment contributes in addition to what has already been contributed by the lower order moments. Information is extracted from orthogonality conditions and a sequential strategy proposed which analyzes the efficiency gains and the coherency of the available information with the new information obtained from incorporating an additional moment into the model