ERC FUNDED PROJECTS

The Virtual Element Method (VEM) is a novel technology for the discretization of partial differential equations (PDEs), that shares the same variational background as the Finite Element Method. First but not only, the VEM responds to the strongly increasing interest in using general polyhedral and polygonal meshes in the approximation of PDEs without the limit of using tetrahedral or hexahedral grids. By avoiding the explicit integration of the shape functions that span the discrete space and introducing an innovative construction of the stiffness matrixes, the VEM acquires very interesting properties and advantages with respect to more standard Galerkin methods, yet still keeping the same coding complexity. For instance, the VEM easily allows for polygonal/polyhedral meshes (even non-conforming) with non-convex elements and possibly with curved faces; it allows for discrete spaces of arbitrary C^k regularity on unstructured meshes. The main scope of the project is to address the recent theoretical challenges posed by VEM and to assess whether this promising technology can achieve a breakthrough in applications. First, the theoretical and computational foundations of VEM will be made stronger. A deeper theoretical insight, supported by a wider numerical experience on benchmark problems, will be developed to gain a better understanding of the method's potentials and set the foundations for more applicative purposes. Second, we will focus our attention on two tough and up-to-date problems of practical interest: large deformation elasticity (where VEM can yield a dramatically more efficient handling of material inclusions, meshing of the domain and grid adaptivity, plus a much stronger robustness with respect to large grid distortions) and the cardiac bidomain model (where VEM can lead to a more accurate domain approximation through MRI data, a flexible refinement/de-refinement procedure along the propagation front, to an exact satisfaction of conservation laws).

980 634 €

Start date: 2016-07-01, End date: 2021-06-30

A growing number of scholars are studying the interactions between cultural values, social and religious norms, institutions, and economic outcomes. The rise of markets, as well as the development of contracts that enable mutually beneficial transactions among agents, are one of the central themes in the literature on long-term economic growth. This project contributes to both strands of literature by studying the invention and development of marine insurance contracts in medieval Italy and their subsequent spread all over Europe. It brings the economic approach to previously unexplored historical data housed in archives in Florence, Genoa, Pisa, Palermo, Prato, and Venice. The interest in the historical origin and development of marine insurance contracts is twofold. First, marine contracts are the “parents” of all the other insurance contracts (e.g., fire, life, health, etc) that were developed in subsequent centuries to cope with risk. Second, their invention, as well as other innovations in business practices in the Middle Ages, contributed to the growth of international trade in subsequent centuries. The key novelty of the project stems from combining contract theory with information from thousands of insurance contracts between 1300 and 1550 to explain why marine insurance developed in medieval Italy and then Europe, to study the empirical determinants of insurance contracts in medieval Italy, and to analyze how medieval merchants coped with adverse selection and moral hazard problems. Most scholars agree that marine insurance was unknown to the ancient world. Italian merchants developed the first insurance contracts and other innovations in business practices during and in the aftermath of the Commercial Revolution that swept Europe from roughly 1275 to about 1325. Marine insurance contracts may have developed as a spin-off of earlier contracts which shifted the risk from one party to another (e.g., sea loan, insurance loan). Alternatively, in the early or mid-fourteenth century, sedentary merchants that provided the capital to travelling merchants invented a new type of contract, when they discovered that the existing contract forms had shortcomings in transferring and dividing sea risk. A sample of the questions that this project will address includes: - Why did insurance contracts and a marine insurance market first develop in medieval times and not earlier despite merchants had to deal with the risks associated with maritime trade since antiquity? - What were the empirical determinants of contract form (e.g., insurance premium) in the medieval insurance market? - How did medieval merchants compute insurance premia without having the formal notion of probability that was developed only in the mid-seventeenth century? - How did medieval merchants cope with the typical problems that plague insurance markets, i.e., adverse selection and moral hazard?

1 113 900 €

Start date: 2012-07-01, End date: 2018-06-30

"Not all new ideas are equally valuable from a social perspective. As the readers of this document know all too well, “picking the winners” is challenging because innovations have highly uncertain outcomes. The aim of this research project is to develop a general theoretical framework to investigate the design of institutions and mechanisms for evaluating new ideas and innovations. The proposed framework examine how these institutions function, draw parallels between them and suggest changes to ensure more accurate evaluation of ideas. Accurate evaluation is of paramount importance because in order for an idea to be successful, it is not enough that the idea be good. It is also necessary that the idea is recognized as good by those who evaluate it. As the evaluation process becomes more accurate, good ideas are more likely to be funded and incentives for the creation of good ideas are enhanced. A key contribution of our framework is a characterization of the role played by evaluating institutions in overcoming the inefficiencies resulting from decentralized interaction. These institutions act as intermediaries between innovators and users, and thus are able to redress the market failure resulting when ideas are evaluated in a more decentralized way. By viewing evaluating institutions through a common lens, we perform a comparative analysis of the workings of such diverse institutions as research funding bodies, government regulators, and screening panels of venture capitalists. With techniques from the economic theory of mechanism design, we intend to characterize the best institutional design for idea evaluation. We then compare this ideal benchmark with actual institutions and characterize how it depends on the primitive ingredients of the environment. Lastly, through empirical and experimental testing, we propose changes to institution design parameters and suggest modifications to the mechanisms created for the purpose of evaluating ideas."

1 142 200 €

Start date: 2012-06-01, End date: 2017-05-31

How does financial market development affect employment, wages and unemployment risk? And how do labor market institutions and workers’ behavior in turn affect corporate policies? These issues are much under-researched, in spite of their prominence in public debate, often ideologically polarized between those who consider finance as socially harmful and those who view it as an efficient allocation machine. Most economic research indicates that financial development raises output growth, but is silent about its effects on the labor market: does it also raise employment and wages? If so, is it at the expense of greater employment risk and inequality? And how does the potential for systemic financial instability affect the answers to these questions? The study of these issues naturally opens also another – equally under-researched – line of inquiry: that concerning the effects of labor relations on financial arrangements. Do corporate investment policies and leverage decisions take into account their own effects on firms’ bargaining position in wage negotiations? And if so, how are these corporate decisions affected by job protection regulation, union density or workers’ protection in bankruptcy? To what extent do companies insure workers against employment risk, and do family and non-family firms differ in this respect? Finally, can labor market competition damage the performance of employees with decision-making responsibilities? For instance, can it induce managers or traders to take excessively risky decisions, by providing them with an escape route once they make mistakes, especially when outcomes are observed long after decisions? This research project purports to break new ground on both sets of issues, using a combination of analytical modelling and empirical analysis, which in some cases will require the collection of entirely new data.

1 873 800 €

Start date: 2012-07-01, End date: 2018-06-30