Functional spaces and functional completion

This paper analyzes the notion of risk-free rate of return as it is present in professional financial practice and in regulatory debates. Using pragmatist approaches in political anthropology and in the anthropology of money and finance, the paper will map the circulation of this concept through three entries, which imply different institutions and practices, connected through common narratives, found in manuals, financial practice, regulatory frameworks and the press, in an assemblage with specific contradictions, fragmentations and taboos.First, in financial formulas, the concept presupposes that state sovereignty will ensure that taxes are used to pay creditors, establishing a financial, moral and political hierarchy between states, which has shifted in Europe in recent years. Second, the concept defines the minimum return that an activity must offer in order to be even considered as a financial asset. The concept works not only as a stabilizer of the definition of “financial value” itself, but also as a principle of discrimination in the allocation of credit by the finance industry. Finally, the concept also refers to concrete assets, such as AAA rated securities, which must be held by financial institutions according to regulation, and the volumes of which fluctuate, creating important regulatory issues.The paper will be to spell out the different temporalities and institutions that are brought together by the concept in its different uses, their connections and disconnections, as a way to question the global political narrative that it allows for, and the alternatives that it precludes

A rescaled method for RBF approximation

In the recent paper [8], a new method to compute stable kernel-based interpolants has been presented. This \textit{rescaled interpolation} method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allow us to consider its error and stability properties

A rescaled method for RBF approximation

A new method to compute stable kernel-based interpolants has been presented by the second and third authors. This rescaled interpolation method combines the standard kernel interpolation with a properly defined rescaling operation, which smooths the oscillations of the interpolant. Although promising, this procedure lacks a systematic theoretical investigation. Through our analysis, this novel method can be understood as standard kernel interpolation by means of a properly rescaled kernel. This point of view allow us to consider its error and stability properties. First, we prove that the method is an instance of the Shepard\u2019s method, when certain weight functions are used. In particular, the method can reproduce constant functions. Second, it is possible to define a modified set of cardinal functions strictly related to the ones of the not-rescaled kernel. Through these functions, we define a Lebesgue function for the rescaled interpolation process, and study its maximum - the Lebesgue constant - in different settings. Also, a preliminary theoretical result on the estimation of the interpolation error is presented. As an application, we couple our method with a partition of unity algorithm. This setting seems to be the most promising, and we illustrate its behavior with some experiments