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Vector displacements expressed in spherical coordinates are proposed. They correspond to electromagnetic fields in vacuum that globally rotate about an axis and display many circular patterns on the surface of a ball. The fields satisfy the set of Maxwell's equations, and some connections with magnetohydrodynamics can also be established. The solutions are extended with continuity outside the ball. In order to avoid peripheral velocities of arbitrary magnitude, as it may happen for a rigid rotating body, they are organized to form successive encapsulated shells, with substructures recalling ball‐bearing assemblies. A recipe for the construction of these solutions is provided by playing with the eigenfunctions of the vector Laplace operator. Some applications relative to astronomy are finally discussed. [ABSTRACT FROM AUTHOR]

We consider an investor that trades continuously and wants to liquidate an initial asset position within a prescribed time interval. As a consequence of his trading activity, during the execution of the liquidation order, the investor has no guarantees that the placed order is executed immediately; it may go unfilled, partially filled or filled in excess. The uncertainty in the execution affects the trading activity of the investor and the asset share price dynamics generating additional sources of noise: the execution risk and the price impact risk, respectively. Assuming the two sources of noise correlated and driven by the cumulative effect of the investor trading strategy, we study the problem of finding the optimal liquidation strategy adopted by the investor in order to maximize the expected revenue resulting from the liquidation. The mathematical model of the liquidation problem presented here extends the model of Almgren and Chriss [Optimal execution of portfolio transactions. J. Risk, 2000, 3(2), 5–39] to include execution and price impact risks. The liquidation problem is modeled as a linear quadratic stochastic optimal control problem with the finite horizon and, under some assumptions about the functional form for the magnitude of execution and price impact risks, is solved explicitly. The derived solution coincides with the optimal trading strategy obtained in the absence of execution uncertainty for an asset price with a modified growth rate. This suggests that the uncertainty in the execution modifies the directional view of the investor about the future growth rate of the asset price. [ABSTRACT FROM AUTHOR]

We investigate the idea of solving calibration problems for stochastic dynamical systems using statistical tests. We consider a specific stochastic dynamical system: the normal SABR model. The SABR model has been introduced in mathematical finance in 2002 by Hagan, Kumar, Lesniewski and Woodward. The model is a system of two stochastic differential equations whose independent variable is time and whose dependent variables are the forward prices/rates and the associated stochastic volatility. The normal SABR model is a special case of the SABR model. The calibration problem for the normal SABR model is an inverse problem that consists in determining the values of the parameters of the model from a set of data. We consider as set of data two different sets of forward prices/rates and we study the resulting calibration problems. Ad hoc statistical tests are developed to solve these calibration problems. Estimates with statistical significance of the parameters of the model are obtained. Let be a constant, we consider multiple independent trajectories of the normal SABR model associated to given initial conditions assigned at time . In the first calibration problem studied the set of the forward prices/rates observed at time in this set of trajectories is used as data sample of a statistical test. The statistical test used to solve this calibration problem is based on some new formulae for the moments of the forward prices/rates variable of the normal SABR model. The second calibration problem studied uses as data sample the observations of the forward prices/rates made on a discrete set of given time values along a single trajectory of the normal SABR model. The statistical test used to solve this second calibration problem is based on the numerical evaluation of some high-dimensional integrals. The results obtained in the study of the normal SABR model are easily extended from mathematical finance to other contexts in science and engineering where stochastic models involving stochastic volatility or stochastic state space models are used. [ABSTRACT FROM AUTHOR]

This paper shows two examples of how the analysis of option pricing problems can lead to computational methods efficiently implemented in parallel. These computational methods outperform 'general purpose' methods (i.e., for example, Monte Carlo, finite differences methods). The GPU implementation of two numerical algorithms to price two specific derivatives (continuous barrier options and realized variance options) is presented. These algorithms are implemented in CUDA subroutines ready to run on Graphics Processing Units (GPUs) and their performance is studied. The realization of these subroutines is motivated by the extensive use of the derivatives considered in the financial markets to hedge or to take risk and by the interest of financial institutions in the use of state of the art hardware and software to speed up the decision process. The performance of these algorithms is measured using the (CPU/GPU) speed up factor, that is using the ratio between the (wall clock) times required to execute the code on a CPU and on a GPU. The choice of the reference CPU and GPU used to evaluate the speed up factors presented is stated. The outstanding performance of the algorithms developed is due to the mathematical properties of the pricing formulae used and to the ad hoc software implementation. In the case of realized variance options when the computation is done in single precision the comparisons between CPU and GPU execution times gives speed up factors of the order of a few hundreds. For barrier options, the corresponding speed up factors are of about fifteen, twenty. The CUDA subroutines to price barrier options and realized variance options can be downloaded from the website . A more general reference to the work in mathematical finance of some of the authors and of their coauthors is the website . [ABSTRACT FROM AUTHOR]

A new method for calibrating the Black-Scholes asset price dynamics model is proposed. The data used to test the calibration problem included observations of asset prices over a finite set of (known) equispaced discrete time values. Statistical tests were used to estimate the statistical significance of the two parameters of the Black-Scholes model: the volatility and the drift. The effects of these estimates on the option pricing problem were investigated. In particular, the pricing of an option with uncertain volatility in the Black-Scholes framework was revisited, and a statistical significance was associated with the price intervals determined using the Black-Scholes-Barenblatt equations. Numerical experiments involving synthetic and real data were presented. The real data considered were the daily closing values of the S&P500 index and the associated European call and put option prices in the year 2005. The method proposed here for calibrating the Black-Scholes dynamics model could be extended to other science and engineering models that may be expressed in terms of stochastic dynamical systems. [ABSTRACT FROM AUTHOR]

Abstract: The superconsistent collocation method is based on collocation nodes which are different from those used to represent the solution. The two grids are chosen in such a way that the continuous and the discrete operators coincide on a space as larger as possible (superconsistency). There are many documented situations in which this technique provides excellent numerical results. Unfortunately very little theory has been developed. Here, a theoretical convergence analysis for the superconsistent discretization of the second derivative operator, when the representation grid is the set of Chebyshev Gauss–Lobatto nodes is carried out. To this end, a suitable quadrature formula is introduced and studied. [Copyright &y& Elsevier]

Studies the scattering of a time harmonic electromagnetic wave that hits Omega when Omega is assumed to be perfectly conducting. Solution to an exterior boundary value vector for the vector Helmholtz equation; Proof of the existence and uniqueness of the solution of the boundary value problem; Numerical method proposed to compute the solution.

New algorithms for the numerical solution of optimization problems involving the l 0 pseudo-norm are proposed. They are designed to use a recently proposed computational methodology that is able to deal numerically with finite, infinite and infinitesimal numbers. This new methodology introduces an infinite unit of measure expressed by the numeral 1 (grossone) and indicating the number of elements of the set I N , of natural numbers. We show how the numerical system built upon 1 and the proposed approximation of the l 0 pseudo-norm in terms of 1 can be successfully used in the solution of elastic net regularization problems and sparse support vector machines classification problems. [ABSTRACT FROM AUTHOR]

Aims: The aim of this work was to assess the effects of a probiotic diet on well‐being of healthy seniors living in boarding and private homes in Marche Region, Italy. In particular, we focused on the modulation of high‐sensitivity C‐reactive protein (HsCRP), intestinal microbiota and short‐chain fatty acids (SCFAs). Methods and Results: Ninety‐seven healthy seniors took part in a double‐blind, placebo‐controlled feeding study (59 fed probiotics, 38 fed placebo) for 6 months. Each volunteer ingested daily one food product or a dietary supplement enriched with Synbio® blend (Synbiotec Srl, Camerino, Italy) or the placebo (control group). Blood and faecal samples were collected before and at the end of the intervention period to perform biochemical and microbiological analyses. The serum HsCRP difference value after 6 months of treatment was significantly higher in the probiotic group than placebo (p < 0.05). After the intervention, a significant increase in faecal lactobacilli and a bifidobacteria increase in more participants were observed in the probiotic group. The 16S NGS analysis on the probiotic group showed a decreasing trend of Proteobacteria at the end of the treatment and conversely, an increasing trend of Actinobacteria and Verrucomicrobia phyla, to which the increase of Akkermansiaceae and Bifidobacteriaceae contributes at the family level. Finally, total short‐chain fatty acids (SCFAs) and butyric acid were significantly higher in the probiotic group at the end of the treatment respect to the beginning. Conclusions: Overall, this study emphasizes the beneficial anti‐inflammageing effect of a prolonged diet based on functional foods enriched with Synbio® through the modulation of the intestinal microbiota and the consequent increase in the SCFA production. Significance and Impact of the Study: Synbio® integration in elderly daily diet may be a preventive strategy to support healthy ageing. [ABSTRACT FROM AUTHOR]

A highly parallelizable numerical method to solve three-dimensional time-dependent acoustic obstacle scattering problems involving passive or smart, furtive, realistic obstacles is presented. ‘‘Realistic’’ obstacles have complex geometries, ‘‘passive’’ obstacles do not react by taking an action to pursue a goal when hit by an incoming wave, and ‘‘smart furtive’’ obstacles, when hit by an incoming wave, pursue the goal of being undetectable by circulating a suitable pressure current on their boundaries. Incoming wave packets containing time-harmonic waves of small wavelengths when compared with the characteristic dimension of the obstacles are considered. The features of the computational method proposed to solve these scattering problems that can be exploited in a parallel and/or distributed computing environment are presented. Numerical experiments involving a simplified version of the NASA space shuttle are discussed. The websites: http://www.econ.univpm.it/ recchioni/scattering/w12, http://www.econ.univpm.it/recchioni/scattering/w14 contain animations and virtual reality applications showing some numerical experiments relative to the problems studied. A more general reference to the work of some of the authors and of their coworkers in acoustic and electromagnetic scattering is the website: http://www.econ. univpm.it/recchioni/scattering. [ABSTRACT FROM AUTHOR]