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.

Essays in Media and Finance

This Ph.D. thesis consists in three research papers focused on the relationship between media industry and the financial sector. The importance of a correct understanding what is the effect of media on financial markets is becoming increasingly important as long as fully informed markets hypothesis has been challenged. Therefore, if financial markets do not have access to complete information, the importance of information professionals, the media, follows. On the other side, another challenge for economic and finance scholar is to understand how financial features are able to influence media and to condition information disclosure. The main aim of this Ph.D. dissertation is to contribute to a better comprehension for both the phenomena. The first paper analyzes the effects of owning equity shares in a newspaper- publishing firm. The main findings show how for a firm being part of the ownership structure of a media firm ends to receive more and better coverage. This confirms the view in which owning a media outlet is a source of conflicts of interest. The second paper focuses on the effect of media-delivered information on financial markets. In the framework of IPO in the U.S. market, we found empirical evidence of a significant effect of the media role in the IPO pricing. Specifically, increasing the quantity and the quality of the coverage increases the first-day returns (i.e. the underpricing). Finally the third paper tries to summarize what has been done in studying the relationship between media and financial industries, putting together contributes from economic, business, and financial scholars. The main finding of this dissertation is therefore to have underlined the importance and the effectiveness of the relationship between media industry and the financial sector, contributing to the stream of research that investigates about the media role and media effectiveness in the financial and business sectors.

Enhanced Mixed Integer Programming Techniques and Routing Problems

Mixed integer programming is up today one of the most widely used techniques for dealing with hard optimization problems. On the one side, many practical optimization problems arising from real-world applications (such as, e.g., scheduling, project planning, transportation, telecommunications, economics and finance, timetabling, etc) can be easily and effectively formulated as Mixed Integer linear Programs (MIPs). On the other hand, 50 and more years of intensive research has dramatically improved on the capability of the current generation of MIP solvers to tackle hard problems in practice. However, many questions are still open and not fully understood, and the mixed integer programming community is still more than active in trying to answer some of these questions. As a consequence, a huge number of papers are continuously developed and new intriguing questions arise every year. When dealing with MIPs, we have to distinguish between two different scenarios. The first one happens when we are asked to handle a general MIP and we cannot assume any special structure for the given problem. In this case, a Linear Programming (LP) relaxation and some integrality requirements are all we have for tackling the problem, and we are ``forced" to use some general purpose techniques. The second one happens when mixed integer programming is used to address a somehow structured problem. In this context, polyhedral analysis and other theoretical and practical considerations are typically exploited to devise some special purpose techniques. This thesis tries to give some insights in both the above mentioned situations. The first part of the work is focused on general purpose cutting planes, which are probably the key ingredient behind the success of the current generation of MIP solvers. Chapter 1 presents a quick overview of the main ingredients of a branch-and-cut algorithm, while Chapter 2 recalls some results from the literature in the context of disjunctive cuts and their connections with Gomory mixed integer cuts. Chapter 3 presents a theoretical and computational investigation of disjunctive cuts. In particular, we analyze the connections between different normalization conditions (i.e., conditions to truncate the cone associated with disjunctive cutting planes) and other crucial aspects as cut rank, cut density and cut strength. We give a theoretical characterization of weak rays of the disjunctive cone that lead to dominated cuts, and propose a practical method to possibly strengthen those cuts arising from such weak extremal solution. Further, we point out how redundant constraints can affect the quality of the generated disjunctive cuts, and discuss possible ways to cope with them. Finally, Chapter 4 presents some preliminary ideas in the context of multiple-row cuts. Very recently, a series of papers have brought the attention to the possibility of generating cuts using more than one row of the simplex tableau at a time. Several interesting theoretical results have been presented in this direction, often revisiting and recalling other important results discovered more than 40 years ago. However, is not clear at all how these results can be exploited in practice. As stated, the chapter is a still work-in-progress and simply presents a possible way for generating two-row cuts from the simplex tableau arising from lattice-free triangles and some preliminary computational results. The second part of the thesis is instead focused on the heuristic and exact exploitation of integer programming techniques for hard combinatorial optimization problems in the context of routing applications. Chapters 5 and 6 present an integer linear programming local search algorithm for Vehicle Routing Problems (VRPs). The overall procedure follows a general destroy-and-repair paradigm (i.e., the current solution is first randomly destroyed and then repaired in the attempt of finding a new improved solution) where a class of exponential neighborhoods are iteratively explored by heuristically solving an integer programming formulation through a general purpose MIP solver. Chapters 7 and 8 deal with exact branch-and-cut methods. Chapter 7 presents an extended formulation for the Traveling Salesman Problem with Time Windows (TSPTW), a generalization of the well known TSP where each node must be visited within a given time window. The polyhedral approaches proposed for this problem in the literature typically follow the one which has been proven to be extremely effective in the classical TSP context. Here we present an overall (quite) general idea which is based on a relaxed discretization of time windows. Such an idea leads to a stronger formulation and to stronger valid inequalities which are then separated within the classical branch-and-cut framework. Finally, Chapter 8 addresses the branch-and-cut in the context of Generalized Minimum Spanning Tree Problems (GMSTPs) (i.e., a class of NP-hard generalizations of the classical minimum spanning tree problem). In this chapter, we show how some basic ideas (and, in particular, the usage of general purpose cutting planes) can be useful to improve on branch-and-cut methods proposed in the literature.

Sanctions and public enforcement of insider trading laws in Europe

The recent financial crisis triggered an increasing demand for financial regulation to counteract the potential negative economic effects of the evermore complex operations and instruments available on financial markets. As a result, insider trading regulation counts amongst the relatively recent but particularly active regulation battles in Europe and overseas. Claims for more transparency and equitable securities markets proliferate, ranging from concerns about investor protection to global market stability. The internationalization of the world’s securities market has challenged traditional notions of regulation and enforcement. Considering that insider trading is currently forbidden all over Europe, this study follows a law and economics approach in identifying how this prohibition should be enforced. More precisely, the study investigates first whether criminal law is necessary under all circumstances to enforce insider trading; second, if it should be introduced at EU level. This study provides evidence of law and economics theoretical logic underlying the legal mechanisms that guide sanctioning and public enforcement of the insider trading prohibition by identifying optimal forms, natures and types of sanctions that effectively induce insider trading deterrence. The analysis further aims to reveal the economic rationality that drives the potential need for harmonization of criminal enforcement of insider trading laws within the European environment by proceeding to a comparative analysis of the current legislations of height selected Member States. This work also assesses the European Union’s most recent initiative through a critical analysis of the proposal for a Directive on criminal sanctions for Market Abuse. Based on the conclusions drawn from its close analysis, the study takes on the challenge of analyzing whether or not the actual European public enforcement of the laws prohibiting insider trading is coherent with the theoretical law and economics recommendations, and how these enforcement practices could be improved.