The Valuative Theory of Foliations

We describe the valuations following infinitely near singular points of a (singular) holomorphic foliation in the complex plane. They appear to be those satisfying a generalization of L'Hopital's rule. With them, we characterize dicritical vector fields, generic simple singularities, the existence of non- convergent solutions, etc. The construction is generalizable to dimension n.Comment: 16 pages, uses package: diagram.te

Power Series Solutions of Non-Linear q-Difference Equations and the Newton-Puiseux Polygon

Adapting the Newton-Puiseux Polygon process to nonlinear q-difference equations of any order and degree, we compute their power series solutions, study the properties of the set of exponents of the solutions and give a bound for their $q-$Gevrey order in terms of the order of the original equation

Knowledge spillovers in neoclassical growth model: an extension with public sector

We propose a framework to analyze convergence between regions, incorporating the public sector and technological knowledge spillovers in the context of a Neoclassical Growth Model. Secondly, we apply novel estimation methods pertaining to the spatial econometrics literature introducing a spatial autoregressive panel data model based on instrumental variables estimation. Additionally, we introduce marginal effects associated with changing explanatory variables. Our model makes it possible to analyze, in terms of convergence, the results obtained in Spanish regions with the policies implemented during the period 1980–2007. The results support the idea that investments in physical, private and public capital, as well as in education have a positive effect on regional development and cohesion. Therefore, we can conclude that it is possible to obtain better results for regional convergence with higher rates of public investment. We also obtain interesting results that confirm the existence of spillover effects in economic growth and public policies, identifying their magnitude and significanc

Forecasting the maximum compensation offer in the automobile BI claims negotiation proces.

Most motor bodily injury (BI) claims are settled by negotiation, with fewer than 5% of cases going to court. A well-defined negotiation strategy is thus very useful for insurance companies. In this paper we assume that the monetary compensation awarded in court is the upper amount to be offered by the insurer in the negotiation process. Using a real database, a log-linear model is implemented to estimate the maximal offer. Non-spherical disturbances are detected. Correlation occurs when various claims are settled in the same judicial verdict. Groupwise heteroscedasticity is due to the influence of the forensic valuation on the final compensation amount. An alternative approximation based on generalized inference theory is applied to estimate confidence intervals on variance components, since classical interval estimates may be unreliable for datasets with unbalanced structures.bodily injury claims compensation, negotiation process, generalized confidence intervals.

Prediction of individual automobile RBNS claim reserves in the context of Solvency II

Automobile bodily injury (BI) claims remain unsettled for a long time after the accident. The estimation of an accurate reserve for Reported But Not Settled (RBNS) claims is therefore vital for insurers. In accordance with the recommendation included in the Solvency II project (CEIOPS, 2007) a statistical model is here implemented for RBNS reserve estimation. Lognormality on empirical compensation cost data is observed for different levels of BI severity. The individual claim provision is estimated by allocating the expected mean compensation for the predicted severity of the victim’s injury, for which the upper bound is also computed. The BI severity is predicted by means of a heteroscedastic multiple choice model, because empirical evidence has found that the variability in the latent severity of injured individuals travelling by car is not constant. It is shown that this methodology can improve the accuracy of RBNS reserve estimation at all stages, as compared to the subjective assessment that has traditionally been made by practitioners.Automobile accident, Solvency II, bodily injury claims, individual RBNS reserve..

Space Decompositions and Solvers for Discontinuous Galerkin Methods

We present a brief overview of the different domain and space decomposition techniques that enter in developing and analyzing solvers for discontinuous Galerkin methods. Emphasis is given to the novel and distinct features that arise when considering DG discretizations over conforming methods. Connections and differences with the conforming approaches are emphasized.Comment: 2 pages 2 figures no table