Bayesian Analysis of Linear Inverse Problems with Applications in Economics and Finance

In my PhD thesis I propose a Bayesian nonparametric estimation method for structural econometric models where the functional parameter of interest describes the economic agent's behavior. The structural parameter is characterized as the solution of a functional equation, or by using more technical words, as the solution of an inverse problem that can be either ill-posed or well-posed. From a Bayesian point of view, the parameter of interest is a random function and the solution to the inference problem is the posterior distribution of this parameter. A regular version of the posterior distribution in functional spaces is characterized. However, the infinite dimension of the considered spaces causes a problem of non continuity of the solution and then a problem of inconsistency, from a frequentist point of view, of the posterior distribution (i.e. problem of ill-posedness). The contribution of this essay is to propose new methods to deal with this problem of ill-posedness. The first one consists in adopting a Tikhonov regularization scheme in the construction of the posterior distribution so that I end up with a new object that I call regularized posterior distribution and that I guess it is solution of the inverse problem. The second approach consists in specifying a prior distribution on the parameter of interest of the g-prior type. Then, I detect a class of models for which the prior distribution is able to correct for the ill-posedness also in infinite dimensional problems. I study asymptotic properties of these proposed solutions and I prove that, under some regularity condition satisfied by the true value of the parameter of interest, they are consistent in a "frequentist" sense. Once I have set the general theory, I apply my bayesian nonparametric methodology to different estimation problems. First, I apply this estimator to deconvolution and to hazard rate, density and regression estimation. Then, I consider the estimation of an Instrumental Regression that is useful in micro-econometrics when we have to deal with problems of endogeneity. Finally, I develop an application in finance: I get the bayesian estimator for the equilibrium asset pricing functional by using the Euler equation defined in the Lucas'(1978) tree-type models.

Synthesis and aplication of linear and macrocyclic nitrogen ligand

Linear and macrocyclic nitrogen ligands have been found wide application during the years. Nitrogen has a much strong association with transition-metal ions because the electron pair is partucularly available for complexing purposes. We started our investigation with the synthesis of new chiral perazamacrocycles containing four pyrrole rings. This ligand was synthesized by the [2+2]condensation of (R,R)-diaminocyclohexane and dipirranedialdehydes and was tested, after a complexation with Cu(OAc)2, in Henry reactions. The best yields (96%) and higher ee’s (96%) were obtained when the meso-substituent on the dipyrrandialdehyde was a methyl group. The positive influence of the pyrrole-containing macrocyclic structure on the efficiency/enantioselectivity of the catalytic system was demonstrated by comparison with the Henry reactions performed using analogous ligands. Henry product was obtain in good yield but only 73% of ee, when the dialdehyde unit was replaced by a triheteroaromatic dialdehye (furan-pyrrol-furan). Another well known macrocyclic ligand is calix[4]pyrrole. We decided to investigate, in collaboration with Neier’s group, the metal-coordinating properties of calix[2]pyrrole[2]pyrrolidine compounds obtained by the reduction of calix[4]pyrrole. We focused our attention on the reduction conditions, and tested different Pd supported (charcoal, grafite) catalysts at different condition. Concerning the synthesis of linear polyamine ligands. We focused our attention to the synthesis of 2-heteroaryl- and 2,5-diheteroarylpyrrolidines. The reductive amination reaction of diarylketones and aryl-substitutedketo-aldehydes with different chiral amines was exploited to prepare a small library of diastereo-enriched substituted pyrrolidines. We have also described a new synthetic route to 1,2-disubstituted 1,2,3,4-tetrahydropyrrole[1,2-a]pyrazines, which involves the diastereoselective addition of Grignard reagents to chiral oxazolidines. The best diastereoselectivity (98:2) was dependent on the nature of both the chiral auxiliary, (S)-1-phenylglycinol, and the nature of the organometallic reagent (MeMgBr).

A farm-level programming model to compare the atmospheric impact of conventional and organic farming

A model is developed to represent the activity of a farm using the method of linear programming. Two are the main components of the model, the balance of soil fertility and the livestock nutrition. According to the first, the farm is supposed to have a total requirement of nitrogen, which is to be accomplished either through internal sources (manure) or through external sources (fertilisers). The second component describes the animal husbandry as having a nutritional requirement which must be satisfied through the internal production of arable crops or the acquisition of feed from the market. The farmer is supposed to maximise total net income from the agricultural and the zoo-technical activities by choosing one rotation among those available for climate and acclivity. The perspective of the analysis is one of a short period: the structure of the farm is supposed to be fixed without possibility to change the allocation of permanent crops and the amount of animal husbandry. The model is integrated with an environmental module that describes the role of the farm within the carbon-nitrogen cycle. On the one hand the farm allows storing carbon through the photosynthesis of the plants and the accumulation of carbon in the soil; on the other some activities of the farm emit greenhouse gases into the atmosphere. The model is tested for some representative farms of the Emilia-Romagna region, showing to be capable to give different results for conventional and organic farming and providing first results concerning the different atmospheric impact. Relevant data about the representative farms and the feasible rotations are extracted from the FADN database, with an integration of the coefficients from the literature.

Fast and accurate numerical solutions in some problems of particle and radiation transport: synthetic acceleration for the method of short characteristics, Doppler-broadened scattering kernel, remote sensing of the cryosphere

The aim of this work is to present various aspects of numerical simulation of particle and radiation transport for industrial and environmental protection applications, to enable the analysis of complex physical processes in a fast, reliable, and efficient way. In the first part we deal with speed-up of numerical simulation of neutron transport for nuclear reactor core analysis. The convergence properties of the source iteration scheme of the Method of Characteristics applied to be heterogeneous structured geometries has been enhanced by means of Boundary Projection Acceleration, enabling the study of 2D and 3D geometries with transport theory without spatial homogenization. The computational performances have been verified with the C5G7 2D and 3D benchmarks, showing a sensible reduction of iterations and CPU time. The second part is devoted to the study of temperature-dependent elastic scattering of neutrons for heavy isotopes near to the thermal zone. A numerical computation of the Doppler convolution of the elastic scattering kernel based on the gas model is presented, for a general energy dependent cross section and scattering law in the center of mass system. The range of integration has been optimized employing a numerical cutoff, allowing a faster numerical evaluation of the convolution integral. Legendre moments of the transfer kernel are subsequently obtained by direct quadrature and a numerical analysis of the convergence is presented. In the third part we focus our attention to remote sensing applications of radiative transfer employed to investigate the Earth's cryosphere. The photon transport equation is applied to simulate reflectivity of glaciers varying the age of the layer of snow or ice, its thickness, the presence or not other underlying layers, the degree of dust included in the snow, creating a framework able to decipher spectral signals collected by orbiting detectors.