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.

Determining the effect of regulation on Microfinance Institutions Financial Self-Sustainability. A Cross-Country Comparison

Microfinance is an initiative which seeks to address financial inclusion, micro-entrepreneurship, and poverty reduction without over burdening governments. However, the current sector of microfinance is still heavily dependent on the good will of donors. The over-reliance on donations is a feature which threatens the long term sustainability of microfinance. Much has been written about this reliance, but research to date hasn’t empirically examined the effect of regulation as a mediator. This is a critical area of study because regulation directly affects Microfinance Institutions’ (MFI) innovation, and innovation is what shapes the future of microfinance. This thesis considers the role that regulation plays in affecting MFI’s and their ability to innovate in products, services and long-term sustainability via access to capital. Interviews were undertaken with stakeholders in MFI’s, NGO’s, Self-Regulating Bodies, and Regulators in India, Pakistan, and Bangladesh. This thesis discusses findings from interviews in relation to regulatory measures regarding financial self-sustainability of MFI’s. The conclusions of this thesis have implications for policy and inform the microfinance literature.

Multi-organ support device for combined extracorporeal carbon dioxide removal and hemofiltration treatments with pump-free solution for ultrafiltration

The use of extracorporeal organ support (ECOS) devices is increasingly widespread, to temporarily sustain or replace the functions of impaired organs in critically ill patients. Among ECOS, respiratory functions are supplied by extracorporeal life support (ECLS) therapies like extracorporeal membrane oxygenation (ECMO) and extracorporeal carbon dioxide removal (ECCO2R), and renal replacement therapies (RRT) are used to support kidney functions. However, the leading cause of mortality in critically ill patients is multi-organ dysfunction syndrome (MODS), which requires a complex therapeutic strategy where extracorporeal treatments are often integrated to pharmacological approach. Recently, the concept of multi-organ support therapy (MOST) has been introduced, and several forms of isolated ECOS devices are sequentially connected to provide simultaneous support to different organ systems. The future of critical illness goes towards the development of extracorporeal devices offering multiple organ support therapies on demand by a single hardware platform, where treatment lines can be used alternately or in conjunction. The aim of this industrial PhD project is to design and validate a device for multi-organ support, developing an auxiliary line for renal replacement therapy (hemofiltration) to be integrated on a platform for ECCO2R. The intended purpose of the ancillary line, which can be connected on demand, is to remove excess fluids by ultrafiltration and achieve volume control by the infusion of a replacement solution, as patients undergoing respiratory support are particularly prone to develop fluid overload. Furthermore, an ultrafiltration regulation system shall be developed using a powered and software-modulated pinch-valve on the effluent line of the hemofilter, proposed as an alternative to the state-of-the-art solution with peristaltic pump.