Multidimensional Setting Research Articles

How to pick your staff? Using data envelopment analysis

Purpose– This purpose of this paper is to present a tool for facilitating personnel selection when multiple heterogeneous human resource managers use multiple criteria. Two problems result from such a situation. First, when multiple criteria are applied, it is unusual for one candidate to dominate the other candidates in all areas, which requires assigning weights to the different criteria to be able to rank the candidates. Second, in a heterogeneous selection committee, finding weights that accurately reflect the individual preferences of all members is difficult.Design/methodology/approach– To deal with the multidimensional setting of selecting personnel, this paper introduces data envelopment analysis with assurance region (DEA-AR) to determine individually optimal weights for each applicant.Findings– DEA-AR leads to a score for each applicant that can serve as a signal for productivity and, thus, for evaluating the candidate. Based on linear programming, DEA-AR not only aggregates multiple dimensions into a single score but also incorporates managers’ preferences. In addition, the procedure is transparent and fair. It seems to be highly appropriate for selecting personnel. Based on a simulated dataset of applicants, the use of DEA-AR for selecting personnel is illustrated and discussed.Originality/value– DEA-AR provides a tool for supporting personnel selection or pre-selection. This model is based on a mechanical procedure and considers managers’ ideas about weights.

A Non-Stationary Model of Dividend Distribution in A Stochastic Interest-Rate Setting

In this paper the solutions to several variants of the so-called dividend-distribution problem in a multi-dimensional setting are studied. In a nutshell, the manager of a firm must balance the retention of earnings (so as to ward off bankruptcy and earn interest) and the distribution of dividends (so as to please the shareholders). A dynamic-programming approach is used, where the state variables are the current levels of cash reserves and of the stochastic short-rate, as well as time. This results in a family of Hamilton-Jacobi-Bellman variational inequalities whose solutions must be approximated numerically. To do so, a finite-element approximation and a time-marching scheme are employed.

Nonparametric estimation of general multivariate tail dependence and applications to financial time series

In order to analyse the entire tail dependence structure among random variables in a multidimensional setting, we present and study several nonparametric estimators of general tail dependence functions. These estimators measure tail dependence in different orthants, complementing the commonly studied positive (lower and upper) tail dependence. This approach is in line with the parametric analysis of general tail dependence. Under this unifying approach the different dependencies are analysed using the associated copulas. We generalise estimators of the lower and upper tail dependence coefficient to the general multivariate tail dependence function and study their statistical properties. Tail dependence measures come as a response to the incapability of the correlation coefficient as an extreme dependence measure. We run a Monte Carlo simulation study to assess the performance of the nonparametric estimators. We also employ selected estimators in two empirical applications to detect and measure the general multivariate non-positive tail dependence in financial data, which popular parametric copula models commonly applied in the financial literature fail to capture.

Research on the Multidimensional Teaching Goal Setting and Implementation of Exhibition Lighting and Illumination Design

Hubei Institute of Fine Arts has been analyzing, sorting and studying the exhibition lighting and illumination design curriculum since the establishment of exhibition design major. Such curriculum includes various multidimensional objectives, such as exploring the design content of lighting effect of spatial form and exhibition props, investigation and estimation of natural and artificial light source as well as conception creation of scenario lighting effect, establishing model with strong lighting and lighting performance, etc. Based on the sorting and analysis of the curriculum system of “Exhibition Lighting and Illumination design” and exampled at excellent students’ works, the multidimensional teaching goal and implementation of exhibition lighting and illumination design were interpreted systematically. This could provide basis for other associated colleges in launching exhibition lighting and illumination design curriculum.

A random set approach to confidence regions with applications to the effective dose with combinations of agents.

The effective dose (ED) is the pharmaceutical dosage required to produce a therapeutic response in a fixed proportion of the patients. When only one drug is considered, the problem is a univariate one and has been well-studied. However, in the multidimensional setting, that is, in the presence of combinations of agents, estimation of the ED becomes more difficult. This study is focused on the plug-in logistic regression estimator of the multidimensional ED. We discuss consistency of such estimators and focus on the problem of simultaneous confidence regions. We develop a bootstrap algorithm to estimate confidence regions for the multidimensional ED. Through simulation, we show that the proposed method gives 95% confidence regions, which have better empirical coverage than the previous method for moderate to large sample sizes. The novel approach is illustrated on a cytotoxicity study on the effect of two toxins in the leukemia cell line HL-60 and a decompression sickness study of the effects of the duration and depth of the dive.

Asymptotic results for over-dispersed operational risk by using the asymptotic expansion method

In this paper, the author considers a new Loss-distribution-approach model, in which the over-dispersed operational risks are modeled by the compound negative binomial process. In the single dimensional case, asymptotic expansion for the quantile of compound negative binomial process is explored for computing the capital charge of a bank for operational risk. Moreover, when the dependence structure between different risk cells is modeled by the Frank copula, this approach is extended to the multi-dimensional setting. A practical example is given to demonstrate the effectiveness of approximation results.

VECTOR-VALUED COHERENT RISK MEASURE PROCESSES

Introduced by Artzner et al. (1998) the axiomatic characterization of a static coherent risk measure was extended by Jouini et al. (2004) in a multi-dimensional setting to the concept of vector-valued risk measures. In this paper, we propose a dynamic version of the vector-valued risk measures in a continuous-time framework. Particular attention is devoted to the choice of a convenient risk space. We provide dual characterization results, we study different notions of time consistency and we give examples of vector-valued risk measure processes.

Co-dependence of extreme events in high frequency FX returns

In this paper, we investigate extreme events in high frequency, multivariate FX returns within a purposely built framework. We generalize univariate tests and concepts to multidimensional settings and employ these novel techniques for parametric and nonparametric analysis. In particular, we investigate and quantify the co-dependence of cross-sectional and intertemporal extreme events. We find evidence of the cubic law of extreme returns, their increasing and asymmetric dependence and of the scaling property of extreme risk in joint symmetric tails.

Characterizing mutual exclusivity as the strongest negative multivariate dependence structure

Mutual exclusivity is an extreme negative dependence structure that was first proposed and studied in Dhaene and Denuit (1999) in the context of insurance risks. In this article, we revisit this notion and present versatile characterizations of mutually exclusive random vectors via their pairwise counter-monotonic behaviour, minimal convex sum property, distributional representation and the characteristic function of the sum of their components. These characterizations highlight the role of mutual exclusivity in generalizing counter-monotonicity as the strongest negative dependence structure in a multi-dimensional setting.

A Modulus-Squared Dirichlet Boundary Condition for Time-Dependent Complex Partial Differential Equations and Its Application to the Nonlinear Schrödinger Equation

An easy to implement modulus-squared Dirichlet (MSD) boundary condition is formulated for numerical simulations of time-dependent complex partial differential equations in multidimensional settings. The MSD boundary condition approximates a constant modulus-squared value of the solution at the boundaries and is defined as $\frac{\partial \Psi}{\partial t}|_b \approx i\,\mbox{Im}[ \frac{1}{\Psi_{b-1}} \frac{\partial \Psi}{\partial t}|_{b-1} ]\,\Psi_b,$ where $\Psi$ is the complex field and the subscripts $b$ and $b-1$ refer to a boundary point and the closest interior point to the boundary, respectively. Application of the MSD boundary condition to simulations of the nonlinear Schrodinger equation is shown, and numerical simulations are performed to demonstrate its usefulness and advantages over other simple boundary conditions.

Multidimensional Affluence in Income and Wealth in the Eurozone - A Cross Country Comparison Using the HFCS

This paper applies multidimensional affluence measures to a new dataset on income and wealth in 15 Eurozone countries. We start our analysis by examining the income and wealth distributions separately for each country, and extend it to a multidimensional setting by considering the joint distribution of income and wealth. The results indicate that the percentage of households affluent both in income and net wealth are less than 10% except in Cyprus, France, Italy and Slovenia. Investigating the joint distributions of income and net wealth yields that France demonstrates a more homogenous distribution of richness among affluent households compared to the other countries in the sample. Portugal demonstrates a higher concentration of richness in the hands of few compared to most of the other countries in the sample. The degree of countries’ affluence rankings differs with respect to the measures of multidimensional affluence considered.

Co-Dependence of Extreme Events in High Frequency FX Returns

In this paper, we investigate extreme events in high frequency, multivariate FX returns within a purposely built framework. We generalize univariate tests and concepts to multidimensional settings and employ these novel techniques for parametric and nonparametric analysis. In particular, we investigate and quantify the co-dependence of cross-sectional and intertemporal extreme events. We find evidence of the cubic law of extreme returns, their increasing and asymmetric dependence and of the scaling property of extreme risk in joint symmetric tails.

Optimized frames and multi-dimensional challenges in time-frequency analysis

The aim of this introductory communication is to present some challenges of the emerging research topics related to uncertainties, optimizations and multi-dimensional settings in the framework of time-frequency analysis. On one hand we study problems related to multivariate high-D Gabor frame constructions and on the other hand we corelate them with the optimal window constructions.

On Error Estimates for Asymptotic Expansions with Malliavin Weights -- Application to Stochastic Volatility Model

This paper proposes a unified method for precise estimates of the error bounds in asymptotic expansions of an option price and its Greeks (sensitivities) under a stochastic volatility model. More generally, we also derive an error estimate for an asymptotic expansion around a partially elliptic diffusion under a multi-dimensional setting, which includes various important models in finance as the special cases.In particular, we take the Malliavin calculus approach, and estimate the error bounds for the Malliavin weights of both the coefficient and the residual terms in the expansions by effectively applying the properties of Kusuoka-Stroock functions.

NOTE ON AN EXTENSION OF AN ASYMPTOTIC EXPANSION SCHEME

This paper presents an extension of a general computational scheme for asymptotic expansions proposed in earlier works by the authors and coworkers. In the earlier works, a new method was developed for the computation of an arbitrary-order expansion with a normal benchmark distribution in a multidimensional diffusion setting. In particular, a new algorithm was proposed for calculating coefficients in an expansion by solving a system of ordinary differential equations. In the present note, by a change of variable technique, and by various ways of setting the perturbation parameters in the expansion, we provide the flexibility of setting the benchmark distribution around which the expansion is made and an automatic way for computation up to any order in the expansion. For instance, we introduce new expansions, called the lognormal expansion and the CEV expansion. We also show some concrete examples with numerical experiments, which imply that a high-order CEV expansion will produce more a precise and stable approximation for option pricing under the SABR model than other approximation methods such as the log-normal expansion and the well-known normal expansion.

A STRENGTHENED FORM OF A GENERAL HARDY-TYPE INEQUALITY OBTAINED VIA SUPERQUADRATICITY AND ITS APPLICATIONS

In this paper, we establish a new refined version of the general Hardy-type inequality utilizing the notion of superquadratic functions. The general result obtained is then applied to some particular one-dimensional and multidimensional settings providing generalizations and refinements of some well-known Hardy-type inequalities. Finally, as another consequence of the main result, we also state and prove a class of improved versions of some Hardy- Hilbert-type inequalities.

MULTIDIMENSIONAL MODELING OF CORONAL RAIN DYNAMICS

We present the first multidimensional, magnetohydrodynamic simulations which capture the initial formation and the long-term sustainment of the enigmatic coronal rain phenomenon. We demonstrate how thermal instability can induce a spectacular display of in-situ forming blob-like condensations which then start their intimate ballet on top of initially linear force-free arcades. Our magnetic arcades host chromospheric, transition region, and coronal plasma. Following coronal rain dynamics for over 80 minutes physical time, we collect enough statistics to quantify blob widths, lengths, velocity distributions, and other characteristics which directly match with modern observational knowledge. Our virtual coronal rain displays the deformation of blobs into $V$-shaped like features, interactions of blobs due to mostly pressure-mediated levitations, and gives the first views on blobs which evaporate in situ, or get siphoned over the apex of the background arcade. Our simulations pave the way for systematic surveys of coronal rain showers in true multidimensional settings, to connect parametrized heating prescriptions with rain statistics, ultimately allowing to quantify the coronal heating input.

Vector-Valued Risk Measure Processes

Introduced by Artzner, Delbaen, Eber and Heath (1998) the axiomatic characterization of a static coherent risk measure was extended by Jouini, Meddeb and Touzi (2004) in a multi-dimensional setting to the concept of vector-valued risk measures. In this paper, we propose a dynamic version of the vector-valued risk measures in a continuous-time framework. Particular attention is devoted to the choice of a convenient risk space. We provide dual characterization results and examples of vector valued risk measure processes.

Hyperbolic wavelet thresholding methods and the curse of dimensionality through the maxiset approach

In this paper we compute the maxisets of some denoising methods (estimators) for multidimensional signals based on thresholding coefficients in hyperbolic wavelet bases. That is, we determine the largest functional space over which the risk of these estimators converges at a chosen rate. In the unidimensional setting, refining the choice of the coefficients that are subject to thresholding by pooling information from geometric structures in the coefficient domain (e.g., vertical blocks) is known to provide ‘large maxisets’. In the multidimensional setting, the situation is less straightforward. In a sense these estimators are much more exposed to the curse of dimensionality. However we identify cases where information pooling has a clear benefit. In particular, we identify some general structural constraints that can be related to compound functional models and to a minimal level of anisotropy.

Approximation in variation by homothetic operators in multidimensional setting

This paper deals with approximation problems in a multidimensional setting for a family of convolution integral operators of homothetic type of the form $$ (T_wf)({s}) = \int_{\mathcal R^N} K_w ({ t}) f({ st}) \,d{ t},~~w>0,~ { s} \in \mathcal R^N; $$ here $\{K_w\}_{w>0}$ are approximate indentities, $\mathcal R:=\mathbb R^+_0$, and $f$ belongs to $BV^{\varphi}(\mathcal R^N)$, the space of functions with bounded $\varphi$-variation on $\mathcal R^N$. The main result of the paper establishes that, if $f$ is $\varphi$-absolutely continuous, there exists $\mu >0$ such that $$ V^{\varphi}[\mu(T_w f-f)]\longrightarrow 0,\ \ \hbox{as}\ w\rightarrow +\infty, $$ where $V^{\varphi}$ denotes the multidimensional $\varphi$-variation introduced in [8]. The rate of approximation is also investigated, by means of suitable Lipschitz classes.