The status of numerical relativity

Numerical relativity has come a long way in the last three decades and is now reaching a state of maturity. We are gaining a deeper understanding of the fundamental theoretical issues related to the field, from the well posedness of the Cauchy problem, to better gauge conditions, improved boundary treatment, and more realistic initial data. There has also been important work both in numerical methods and software engineering. All these developments have come together to allow the construction of several advanced fully three-dimensional codes capable of dealing with both matter and black holes. In this manuscript I make a brief review the current status of the field.Comment: Report on plenary talk at the 17th International Conference on General Relativity and Gravitation (GR17), held at Dublin, Ireland, july 2004. Latex, 20 pages, 5 figure

The Equivalence of Strict Liability and Negligence Rule: A « Trompe l'œil » Perspective

This paper analyzes the difficulties of comparing the respective effectiveness of two among the most important liability regimes in tort law: rule of negligence and strict liability. Starting from the standard Shavellian unilateral accident scheme, I show that matching up liability regime on their capacity to provide the highest level of safety is ineffective. This demonstration lies on two components. The first one gathers some results drawn from literature that introduces uncertainty. The second one takes into consideration the beliefs of agents and their aversion to ambiguity. The model applies uncertainty to the level of maximum damage. This demonstration reinforces the previous result. Hence, both regimes apply on specific tort question and comparing their individual efficiency needs to call for other components as the transaction costs associated to the burden of evidence, the fairness between victims and injurers, etc.Strict Liability, Negligence Rule, Ambiguity Theory, Uncertainty, Accident Model

On the decomposition of Generalized Additive Independence models

The GAI (Generalized Additive Independence) model proposed by Fishburn is a generalization of the additive utility model, which need not satisfy mutual preferential independence. Its great generality makes however its application and study difficult. We consider a significant subclass of GAI models, namely the discrete 2-additive GAI models, and provide for this class a decomposition into nonnegative monotone terms. This decomposition allows a reduction from exponential to quadratic complexity in any optimization problem involving discrete 2-additive models, making them usable in practice

Liquidity Provision, Ambiguous Asset Returns and the Financial Crisis

For an economy with dysfunctional intertemporal financial markets the financial sector is modelled as a competitive banking sector oering deposit contracts. In a setting similar to Allen and Gale (1998) properties of the optimal liquidity provision are analyzed for illiquid assets with ambiguous returns. In the context of the model, ambiguity | i.e. incalculable risk | leads to dynamically inconsistent investor behaviour. If the financial sector fails to recognize the presence of ambiguity, unanticipated fundamental crises may occur, which are incorrectly blamed on investors 'loosing their nerves' and 'panicing'. The basic mechanism of the current financial crisis resembles a banking panic in the presence of ambiguous asset returns. The combination of providing additional liquidity and supporting distressed financial institutions implements the regulatory policy suggested by the model. A credible commitment to such 'bail-out policy' does not create a moral hazard problem. Rather, it implements the second best efficient outcome by discouraging excessive caution. Reducing ambiguity by increasing stability, transparency and predictability | as suggested by ordo-liberalism and the 'Freiburger Schule’ | enhances ex-ante welfare.Financial Intermediation, Liquidity, Ambiguity, Choquet Expected Utility, Financial Crisis