Maximum principle, mean value operators and quasi boundedness in non-euclidean settings

This work deals with some classes of linear second order partial differential operators with non-negative characteristic form and underlying non- Euclidean structures. These structures are determined by families of locally Lipschitz-continuous vector fields in RN, generating metric spaces of Carnot- Carath´eodory type. The Carnot-Carath´eodory metric related to a family {Xj}j=1,...,m is the control distance obtained by minimizing the time needed to go from two points along piecewise trajectories of vector fields. We are mainly interested in the causes in which a Sobolev-type inequality holds with respect to the X-gradient, and/or the X-control distance is Doubling with respect to the Lebesgue measure in RN. This study is divided into three parts (each corresponding to a chapter), and the subject of each one is a class of operators that includes the class of the subsequent one. In the first chapter, after recalling “X-ellipticity” and related concepts introduced by Kogoj and Lanconelli in [KL00], we show a Maximum Principle for linear second order differential operators for which we only assume a Sobolev-type inequality together with a lower terms summability. Adding some crucial hypotheses on measure and on vector fields (Doubling property and Poincar´e inequality), we will be able to obtain some Liouville-type results. This chapter is based on the paper [GL03] by Guti´errez and Lanconelli. In the second chapter we treat some ultraparabolic equations on Lie groups. In this case RN is the support of a Lie group, and moreover we require that vector fields satisfy left invariance. After recalling some results of Cinti [Cin07] about this class of operators and associated potential theory, we prove a scalar convexity for mean-value operators of L-subharmonic functions, where L is our differential operator. In the third chapter we prove a necessary and sufficient condition of regularity, for boundary points, for Dirichlet problem on an open subset of RN related to sub-Laplacian. On a Carnot group we give the essential background for this type of operator, and introduce the notion of “quasi-boundedness”. Then we show the strict relationship between this notion, the fundamental solution of the given operator, and the regularity of the boundary points.

Estimation of Quasi-Rational DSGE Models

Small-scale dynamic stochastic general equilibrium have been treated as the benchmark of much of the monetary policy literature, given their ability to explain the impact of monetary policy on output, inflation and financial markets. One cause of the empirical failure of New Keynesian models is partially due to the Rational Expectations (RE) paradigm, which entails a tight structure on the dynamics of the system. Under this hypothesis, the agents are assumed to know the data genereting process. In this paper, we propose the econometric analysis of New Keynesian DSGE models under an alternative expectations generating paradigm, which can be regarded as an intermediate position between rational expectations and learning, nameley an adapted version of the "Quasi-Rational" Expectatations (QRE) hypothesis. Given the agents' statistical model, we build a pseudo-structural form from the baseline system of Euler equations, imposing that the length of the reduced form is the same as in the `best' statistical model.

Essays in Financial Econometrics

The first paper sheds light on the informational content of high frequency data and daily data. I assess the economic value of the two family models comparing their performance in forecasting asset volatility through the Value at Risk metric. In running the comparison this paper introduces two key assumptions: jumps in prices and leverage effect in volatility dynamics. Findings suggest that high frequency data models do not exhibit a superior performance over daily data models. In the second paper, building on Majewski et al. (2015), I propose an affine-discrete time model, labeled VARG-J, which is characterized by a multifactor volatility specification. In the VARG-J model volatility experiences periods of extreme movements through a jump factor modeled as an Autoregressive Gamma Zero process. The estimation under historical measure is done by quasi-maximum likelihood and the Extended Kalman Filter. This strategy allows to filter out both volatility factors introducing a measurement equation that relates the Realized Volatility to latent volatility. The risk premia parameters are calibrated using call options written on S&P500 Index. The results clearly illustrate the important contribution of the jump factor in the pricing performance of options and the economic significance of the volatility jump risk premia. In the third paper, I analyze whether there is empirical evidence of contagion at the bank level, measuring the direction and the size of contagion transmission between European markets. In order to understand and quantify the contagion transmission on banking market, I estimate the econometric model by Aït-Sahalia et al. (2015) in which contagion is defined as the within and between countries transmission of shocks and asset returns are directly modeled as a Hawkes jump diffusion process. The empirical analysis indicates that there is a clear evidence of contagion from Greece to European countries as well as self-contagion in all countries.

Mode-I fracture parameters of quasi-brittle materials: direct evaluation using DIC and relationship with Mode-II interfacial parameters

The objective of this thesis is the investigation of the Mode-I fracture mechanics parameters of quasi-brittle materials to shed light onto the influence of the width and size of the specimen on the fracture response of notched beams. To further the knowledge on the fracture process, 3D digital image correlation (DIC) was employed. A new method is proposed to determine experimentally the critical value of the crack opening, which is then used to determine the size of the fracture process zone (FPZ). In addition, the Mode-I fracture mechanics parameters are compared with the Mode-II interfacial properties of composites materials that feature as matrices the quasi-brittle materials studied in Mode-I conditions. To investigate the Mode II fracture parameters, single-lap direct shear tests are performed. Notched concrete beams with six cross-sections has been tested using a three-point bending (TPB) test set-up (Mode-I fracture mechanics). Two depths and three widths of the beam are considered. In addition to concrete beams, alkali-activated mortar beams (AAMs) that differ by the type and size of the aggregates have been tested using the same TPB set-up. Two dimensions of AAMs are considered. The load-deflection response obtained from DIC is compared with the load-deflection response obtained from the readings of two linear variable displacement transformers (LVDT). Load responses, peak loads, strain profiles along the ligament from DIC, fracture energy and failure modes of TPB tests are discussed. The Mode-II problem is investigated by testing steel reinforced grout (SRG) composites bonded to masonry and concrete elements under single-lap direct shear tests. Two types of anchorage systems are proposed for SRG reinforced masonry and concrete element to study their effectiveness. An indirect method is proposed to find the interfacial properties, compare them with the Mode-I fracture properties of the matrix and to model the effect of the anchorage.

The United Nations 'quasi-prosecutorial' investigative mechanisms: assessing a new institutional model in the international criminal justice landscape

This work aims to provide a theoretical examination of three recently created bodies of the United Nations mandated to investigate the alleged international crimes committed in Syria (IIIM), Iraq (UNITAD) and Myanmar (IIMM). Established as a compromise solution in the paralysis of international criminal jurisdictions, these essentially overlapping entities have been depicted as a ‘new generation’ of UN investigative mechanisms. While non-judicial in nature, they depart indeed from traditional commissions of inquiry in several respects due to their increased criminal or ‘quasi-prosecutorial’ character. After clarifying their legal basis and different mandating authorities, a comparative institutional analysis is thus carried out in order to ascertain whether these ‘mechanisms’ can be said to effectively represent a new institutional model. Through an in-depth assessment of their mandates, the thesis is also intended to outline both the strengths and the criticalities of these organs. Given their aim to facilitate criminal proceedings by sharing information and case files, it is suggested that more attention shall be paid to the position of the person under investigation. To this end, some proposals are made in order to enhance the mechanisms’ frameworks, especially from the angle of procedural safeguards. As a third aspect, the cooperation with judicial authorities is explored, in order to shed light on the actors involved, the relevant legal instruments and the possible obstacles, in particular from a human rights perspective. Ultimately, drawing from the detected issues, the thesis seeks to identify some lessons learned which could be taken into account in case of creation of new ad hoc investigative mechanisms or of a permanent institution of this kind.

Essays in Gender Economics

This thesis consists of three papers on gender economics. Chapter 1 studies whether people dislike collaborating with someone who corrects them and whether the dislike is stronger when that person is a woman. Having a good relationship with colleagues is integral in group work, potentially leading to successful collaborations. However, there are occasions when people have to correct their colleagues. Using a quasi-laboratory experiment, I find that people, including those with high productivity, are less willing to collaborate with a person who has corrected them even if the correction improves group performance. In addition, I find suggestive evidence that men respond more negatively to women’s corrections, which is not driven by their beliefs about the difference in women’s and men’s abilities. These findings suggest that there is a behavioral bias in group work that distorts the optimal selection of talents and penalizes those who correct others’ mistakes, and the distortion may be stronger when women correct men. Chapter 2 studies the role of gender and cognitive skills on other peoples’ generosity. Using a novel experimental design where I exogenously vary gender and cognitive skills and sufficiently powered analysis, I find neither the two attributes nor their interactions affect other people’s generosity; if anything, people are more generous to women with high potential. Chapter 3 studies how increased legal tolerance toward domestic violence affects married women’s welfare using the domestic violence decriminalization bill introduced to the Russian national congress in 2016. Using difference-in-differences and flexibly controlling for macroeconomic shocks, I find that the bill decreased married women’s life satisfaction and increased depression, especially among those with a college degree and a highly qualified white-collar occupation supposed to be more sensitive to gender regressive atmosphere. Consistent with this conjecture, people became more tolerant toward general and domestic violence after the bill.