Optimal posting price of limit orders: learning by trading

We model a trader interacting with a continuous market as an iterative algorithm that adjusts limit prices at a given rhythm and propose a procedure to minimize trading costs. We prove the $a.s.$ convergence of the algorithm under assumptions on the cost function and give some practical criteria on model parameters to ensure that the conditions to use the algorithm are met (notably, using the co-monotony principle). We illustrate our results with numerical experiments on both simulated and market data.     

Efficient portfolios in financial markets with proportional transaction costs

In this article, we characterize efficient portfolios, i.e. portfolios which are optimal for at least one rational agent, in a very general multi-currency financial market model with proportional transaction costs. In our setting, transaction costs may be random, time-dependent, have jumps and the preferences of the agents are modeled by multivariate expected utility functions. We provide a complete characterization of efficient portfolios, generalizing earlier results of Dybvig (Rev Financ Stud 1:67–88, 1988) and Jouini and Kallal (J Econ Theory 66: 178–197, 1995). We basically show that a portfolio is efficient if and only if it is cyclically anticomonotonic with respect to at least one consistent price system that prices it. Finally, we introduce the notion of utility price of a given contingent claim as the minimal amount of a given initial portfolio allowing any agent to reach the claim by trading, and give a dual representation of it as the largest proportion of the market price necessary for all agents to reach the same expected utility level.     

Conceptualizing inquiry-based education in mathematics

The terms inquiry-based learning and inquiry-based education have appeared with increasing frequency in educational policy and curriculum documents related to mathematics and science education over the past decade, indicating a major educational trend. We go back to the origin of inquiry as a pedagogical concept in the work of Dewey (e.g. 1916, 1938) to analyse and discuss its migration to science and mathematics education. For conceptualizing inquiry-based mathematics education (IBME) it is important to analyse how this concept resonates with already well-established theoretical frameworks in mathematics education. Six such frameworks are analysed from the perspective of inquiry: the problem-solving tradition, the theory of didactical situations, the realistic mathematics education programme, the mathematical modelling perspective, the anthropological theory of didactics, and the dialogical and critical approach to mathematics education. In an appendix these frameworks are illustrated with paradigmatic examples of teaching activities with inquiry elements. The paper is rounded off with a list of ten concerns for the development and implementation of IBME.     

Variable Selection in Varying-Coefficient Models Using P-Splines

In this article, we consider nonparametric smoothing and variable selection in varying-coefficient models. Varying-coefficient models are commonly used for analyzing the time-dependent effects of covariates on responses measured repeatedly (such as longitudinal data). We present the P-spline estimator in this context and show its estimation consistency for a diverging number of knots (or B-spline basis functions). The combination of P-splines with nonnegative garrote (which is a variable selection method) leads to good estimation and variable selection. Moreover, we consider APSO (additive P-spline selection operator), which combines a P-spline penalty with a regularization penalty, and show its estimation and variable selection consistency. The methods are illustrated with a simulation study and real-data examples. The proofs of the theoretical results as well as one of the real-data examples are provided in the online supplementary materials.     

Cocharacters of Bilinear Mappings and Graded Matrices

Let M _k (F) be the algebra of k ×k matrices over a field F of characteristic 0. If G is any group, we endow M _k (F) with the elementary grading induced by the k-tuple (1,...,1,g) where g?∈?G, g ²?≠?1. Then the graded identities of M _k (F) depending only on variables of homogeneous degree g and g ^???1 are obtained by a natural translation of the identities of bilinear mappings (see Bahturin and Drensky, Linear Algebra Appl 369:95–112, 2003). Here we study such identities by means of the representation theory of the symmetric group. We act with two copies of the symmetric group on a space of multilinear graded polynomials of homogeneous degree g and g ^???1 and we find an explicit decomposition of the corresponding graded cocharacter into irreducibles.     

A collocation method for the numerical solution of a two dimensional integral equation using a quadratic spline quasi-interpolant

In this paper, we propose an interesting method for approximating the solution of a two dimensional second kind equation with a smooth kernel using a bivariate quadratic spline quasi-interpolant (abbr. QI) defined on a uniform criss-cross triangulation of a bounded rectangle. We study the approximation errors of this method together with its Sloan’s iterated version and we illustrate the theoretical results by some numerical examples.     

On the Recurrence Set of Planar Markov Random Walks

In this paper, we investigate properties of recurrent planar Markov random walks. More precisely, we study the set of recurrence points with the use of local limit theorems. The Nagaev–Guivarc’h spectral method provides several examples for which these local limit theorems are satisfied as soon as some (standard or non-standard) central limit theorem and some non-sublattice assumption hold.     

Structural and optical properties of pulsed laser deposited ZnO thin films

Nanocrystalline ZnO thin films were grown by means of pulsed laser deposition. The ablation process was carried out at relatively low background oxygen gas pressure (10 Pa) and by varying the substrate temperature up to 600 °C. Information on the structural and morphological properties of the deposited thin films have been obtained by means of X-ray photoelectron, Raman spectroscopies, X-ray diffraction (XRD) and atomic force microscopy (AFM). The results showed that all the deposited films are sub-stoichiometric in oxygen and with a hexagonal wurtzite crystalline structure, characterized by features of some tens of nanometers in size. An improvement of the films' crystalline quality was observed for the deposition temperature of 300 °C while the further increase of the deposition temperature up to 600 °C induces a worsening of the material's structural properties with the development of a large amount of nanoparticle's clusters. The analysis of the XRD patterns shows a growth crystallographic preferential direction as a function of the deposition temperature, in agreement with the appearance of the only E₂ optical phonon mode in the Raman spectra. Such findings are compatible with the changes observed in the photoluminescent (PL) optical response and was related to the modification of the ZnO thin film structural quality.     

Hyperfine interactions, charge compensation mechanisms, and the distribution of tin dopant cations in rare-earth orthochromites RCrO3 (R = Sm, Eu, Gd, Ho)

The reduction in the squared cosine of angle θ of the Cr-O-Cr bond in the Sm-Ho series in samples containing Sn⁴⁺ ions in the Cr³⁺ position in the crystallite bulk is accompanied by a linear increase in hyperfine field H _{T→0 K} at ¹¹⁹Sn nuclei. Upon annealing in H₂, tin attains oxidation state +2 occupying the Cr³⁺ and R ³⁺ positions on the surfaces of particles. Mössbauer measurements in situ at 100 K do not reveal the spin polarization of Sn²⁺, but this polarization does manifest itself for part of the daughter Sn⁴⁺ ions formed when samples come into contact with air.     

Investigation of design parameters in ultrasound reactors with confined channels

This paper presents a three-dimensional numercial simulation of sonochemical degradation upon cavitational activity. The model relates the simulation of the acoustic pressure distribution to the sonochemical reaction rate. As a case study, the thermal degradation of carbon tetrachloride during sonication is studied in a tubular milliscale reactor. The model is used to optimize the reactor diameter, ultrasound frequency and power dissipated to the ultrasound transducers. The results indicate that multiple transducers at a moderate power level are more efficient than one transducer with high power level. Furthermore, the average cavity volume fraction is proposed as a reaction independent parameter to estimate the optimal reactor design. Within the results obtained in this paper, it appears possible to optimise reactor design based on this parameter.