Great Expectations. Part II: Generalized Expected Utility as a Universal Decision Rule

Many different rules for decision making have been introduced in the literature. We show that a notion of generalized expected utility proposed in Part I of this paper is a universal decision rule, in the sense that it can represent essentially all other decision rules.Comment: Preliminary version appears in Proc. 18th International Joint Conference on AI (IJCAI), 2003, pp. 297-30

Essays on default, entrepreneurship, and institutional arrangements

This dissertation consists of three chapters on the implications of the personal default option on the economy. In the first two chapters, I analyze how credit constraints faced by entrepreneurs are shaped by the legal environment for default that they face. In the third chapter, I explore the welfare implications of allowing financial intermediaries to charge different interest rates according to perceived probabilities of consumer bankruptcy. In the first chapter, I build a model where agents can pick a career and decide whether to default on their mortgage. The purpose of this model is to analyze the interaction between these decisions and the existence of different legal environments, regarding the degree of recourse that lenders have over the borrowers’ assets. The model yields three basic predictions. First, as lenders have more recourse, the cost of default for the borrower increases and default becomes less frequent. Second, as lenders have more recourse, the entrepreneurship threshold (i.e. the amount of home equity a homeowner requires to become an entrepreneur) also increases. Third, where lenders have relatively less recourse, the size of the entrepreneurship threshold reduction due to a house price increase is larger. In the second chapter I test the validity of the third prediction of the model, which encompasses the other two. Using U.S. data, I find that the margins of creation for small young firms responded strongly to the increase in house prices between 2000 and 2007. This effect was driven by those areas where mortgage default is relatively less costly (less recourse). This link between house prices and entrepreneurial activity becomes weaker after the Great Recession. The third chapter explores the effects of allowing financial intermediaries to charge different interest rates according to the debt profile of agents. It also studies the welfare implications of different bankruptcy schemes and those associated with removing the default option. My findings indicate that allowing for price discrimination and removing the bankruptcy option are both desirable. However, the welfare gain from a more stringent bankruptcy regulation is negligible compared to those of removing the bankruptcy option and allowing discrimination

Specification-driven test generation for model transformations

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-642-30476-7_3Proceedings of 5th International Conference, ICMT 2012, Prague, Czech Republic, May 28-29, 2012Testing model transformations poses several challenges, among them the automatic generation of appropriate input test models and the specification of oracle functions. Most approaches to the generation of input models ensure a certain level of source meta-model coverage, whereas the oracle functions are frequently defined using query or graph languages. Both tasks are usually performed independently regardless their common purpose, and sometimes there is a gap between the properties exhibited by the generated input models and those demanded to the transformations (as given by the oracles). Recently, we proposed a formal specification language for the declarative formulation of transformation properties (invariants, pre- and postconditions) from which we generated partial oracle functions that facilitate testing of the transformations. Here we extend the usage of our specification language for the automated generation of input test models by constraint solving. The testing process becomes more intentional because the generated models ensure a certain coverage of the interesting properties of the transformation. Moreover, we use the same specification to consistently derive both the input test models and the oracle functions.Work funded by the Spanish Ministry of Economy and Competitivity (TIN2011-24139) and by the R&D programme of Madrid Region (S2009/TIC-1650

Aspects of quadratic optimization - nonconvexity, uncertainty, and applications

Quadratic Optimization (QO) has been studied extensively in the literature due to its application in real-life problems. This thesis deals with two complicated aspects of QO problems, namely nonconvexity and uncertainty. A nonconvex QO problem is intractable in general. The first part of this thesis presents methods to approximate a nonconvex QP problem. Another important aspect of a QO problem is taking into account uncertainties in the parameters since they are mostly approximated/estimated from data. The second part of the thesis contains analyses of two methods that deal with uncertainties in a convex QO problem, namely Static and Adjustable Robust Optimization problems. To test the methods proposed in this thesis, the following three real-life applications have been considered: pooling problem, portfolio problem, and norm approximation problem

Conjugacy and centralisers in Thompson's group T

PhD ThesisThe Thompson family of groups F < T < V are well-known as interesting (counter-) examples in group theory. Working algebraically with these objects is difficult, and yet the groups are computationally tractable. For instance, T and V are infinite simple groups; despite this, both are finitely presented. This thesis studies the middle group T, using the piecewise-linear function point of view. We present a solution to the conjugacy problem in this group, adapting the approach of Kassabov and Matucci1 to 1 Kassabov and Matucci 2012. the same problem in F. Conjugacy of elements in T was shown2 to 2 Belk and Matucci 2014. be decidable by Belk and Matucci; however our approach constructs explicit conjugators (when they exist). Later, we refine the description given by Matucci3 of nontorsion elements’ centralisers in T. 3 Matucci 2008, Chapter 7. * * * The first chapter introduces the world of Thompson’s groups. The sections on cyclic order, the generalised groups PLS,G and groupoid PL2, and on the Cantor space are particularly important for readers interested in the rest of the thesis. The second chapter discusses Thompson’s groups from a dynamical point of view. We summarise how F, T and V rerrange the interval, noting the distinction between dyadic and nondyadic points. Focussing on T, we introduce the rotation number and explain what we can learn from it. Amidst all this we present a number of intermediate results, forming a toolkit for use in later chapters. The third chapter studies conjugacy in T. We narrow the search space by finding constraints that a conjugator must satisfy. Next, we break the conjugacy problem into a search for a coarse and fine conjugator, the product of which—if they exist—is a bona fide conjugator. We solve these search problems,4 and thus solve the conjugacy problem in T. 4 Lemma 3.3.2 and Algorithms 3.3.5 and 3.4.8. In the fourth chapter, we study element centralisers in T via a particular group extension. We focus on nontorsion elements, providing small details missing from Matucci’s proof which identifies the extension’s kernel.5 We explain how to find the size of the extension’s quotient, by 5 Theorem 4.2.1 and Remark 4.2.2. reducing the problem to a search for coarse conjugators.6 6 Algorithm 4.2.3. The final chapter describes the extension structure of CT(α) in more detail.7 We do so by classifying α into one of four cases. In all but 7 Section 5.2. one case, this extension splits (as a wreath or direct product); in the remaining case, we identify8 exactly when the extension splits (again as 8 See Proposition 5.2.15 and the summary in in Theorem 5.3.2. a wreath product). In each case, we describe the centraliser’s structure9 9 Proposition 5.2.17. in terms of integer parameters. We then show how to construct10 an 10 Corollaries 5.2.6, 5.2.16, 5.2.18, 5.2.23 element of T whose centraliser has a given list of parameters

Formal verification: further complexity issues and applications

Prof. Giacomo Cioffi (Università di Roma "La Sapienza"), Prof. Fabio Panzieri (Università di Bologna), Dott.ssa Carla Limongelli (Università di Roma Tre)

Specification-driven model transformation testing

The final publication is available at Springer via http://dx.doi.org/10.1007/s10270-013-0369-xTesting model transformations poses several challenges, among them the automatic generation of appropriate input test models and the specification of oracle functions. Most approaches for the generation of input models ensure a certain coverage of the source meta-model or the transformation implementation code, whereas oracle functions are frequently defined using query or graph languages. However, these two tasks are usually performed independently regardless of their common purpose, and sometimes, there is a gap between the properties exhibited by the generated input models and those considered by the transformations. Recently, we proposed a formal specification language for the declarative formulation of transformation properties (by means of invariants, pre-, and postconditions) from which we generated partial oracle functions used for transformation testing. Here, we extend the usage of our specification language for the automated generation of input test models by SAT solving. The testing process becomes more intentional because the generated models ensure a certain coverage of the transformation requirements. Moreover, we use the same specification to consistently derive both the input test models and the oracle functions. A set of experiments is presented, aimed at measuring the efficacy of our technique.We thank the referees for their useful comments. This work has been sponsored by the Spanish Ministry of Science and Innovation with project “Go-Lite” (TIN2011-24139), by the R&D program of the Community of Madrid with project “e- Madrid” (S2009/TIC-1650), and by the German Research Foundation (DFG) within the Reinhart Koselleck project (DR 287/23-1)