对数收益率的偏斜Logistic分布与VaR估计

本文通过直方图和Q-Q图的直观方法展示了上证指数和深证指数的对数收益率具有尖峰厚尾和偏斜的分布特征,利用Shapiro-Wilk正态性检验和Kolmogorov-Smirnov检验等方法检验了对数收益率的分布与正态分布有显著性差异,并以较大的概率水平接受了对数收益率服从偏斜Logistic分布,同时给出了基于偏斜Logistic分布的VaR风险量的估计,结果显示上证指数的风险小于深证指数的风险。     

Spectra of a class of self-affine measures

In the present paper we will study the spectral property of a class of self-affine measures under the condition of compatible pair. We first answer a question of Dutkay and Jorgensen concerning the relationship between spectral self-affine measure and compatible pair. We then consider the spectra of Bernoulli convolutions and obtain a sharp result which extends the corresponding result of Jorgensen, Kornelson and Shuman. Finally, we provide a structural property for the integer spectrum of a spectral self-affine measure.     

A bargaining game model for measuring performance of two-stage network structures

Data envelopment analysis (DEA) is a method for measuring the efficiency of peer decision making units (DMUs), where the internal structures of DMUs are treated as a black-box. Recently DEA has been extended to examine the efficiency of DMUs that have two-stage network structures or processes, where all the outputs from the first stage are intermediate measures that make up the inputs to the second stage. The resulting two-stage DEA model not only provides an overall efficiency score for the entire process, but also yields an efficiency score for each of the individual stages. The current paper develops a Nash bargaining game model to measure the performance of DMUs that have a two-stage structure. Under Nash bargaining theory, the two stages are viewed as players and the DEA efficiency model is a cooperative game model. It is shown that when only one intermediate measure exists between the two stages, our newly developed Nash bargaining game approach yields the same results as applying the standard DEA approach to each stage separately. Two real world data sets are used to demonstrate our bargaining game model.     

An attribute weight based feedback model for multiple attributive group decision analysis problems with group consensus requirements in evidential reasoning context

In an evidential reasoning context, a group consensus (GC) based approach can model multiple attributive group decision analysis problems with GC requirements. The predefined GC is reached through several rounds of group analysis and discussion (GAD) in the approach. However, the GAD with no guidance may not be the most appropriate way to reach the predefined GC because several rounds of GAD will spend a lot of time of all experts and yet cannot help them to effectively emphasize on the assessments which primarily damage the GC. In this paper, an attribute weight based feedback model is constructed to effectively identify the assessments primarily damaging the GC and accelerate the GC convergence. Considering important attributes with the weights more than or at least equal to the mean of the weights of all attributes, the feedback model constructs identification rules to identify the assessments damaging the GC for the experts to renew. In addition, a suggestion rule is introduced to generate appropriate recommendations for the experts to renew their identified assessments. The identification rules are constructed at three levels including the attribute, alternative and global levels. The feedback model is used to solve an engineering project management software selection problem to demonstrate its detailed implementation process, its validity and applicability, and its advantages compared with the GC based approach.     

基于未确知测度理论的工业企业经济效益评价

介绍了工业企业经济效益评价的经济指标,建立了基于未确知测度理论的多属性综合评价方法.在确定各评价对象的属性权重时,采用熵值法这一客观性方法来确定.通过实例,将这种方法应用于具体的工业企业经济效益的评价,为评价企业经济效益提供了一种量化处理的方法,从而能够更直观、更合理地分析评价企业的经济效益状况.     

Completely mixed state is a critical point for three-qubit entanglement

Pure three-qubit states have five algebraically independent and one algebraically dependent polynomial invariants under local unitary transformations and an arbitrary entanglement measure is a function of these six invariants. It is shown that if the reduced density operator of a some qubit is a multiple of the unit operator, than the geometric entanglement measure of the pure three-qubit state is absolutely independent of the polynomial invariants and is a constant for such tripartite states. Hence a one-particle completely mixed state is a critical point for the geometric measure of entanglement.     

时延耦合自主个体的一致性问题

考察了同时具有通信时延和输入时延的多自主个体的耦合一致性问题.利用频域分析方法,分别得到了一阶和二阶耦合自主个体渐近达到一致的充分条件,该条件与输入时延、通信时延以及控制参数有关.仿真结果证明了结论的正确性. 关键词： 耦合自主个体 输入时延 通信时延 一致性     

A spectral similarity measure using Bayesian statistics

A spectral similarity measure was developed that can differentiate subtle differences between two spectra. The spectra are digitalized into a vector. The difference between the two spectra is defined by a difference vector, which is one spectrum minus the other. The spectral similarity measure is transformed into a hypothesis test of the similarities and differences between the two spectra. The scalar mean of the difference vector is used as the statistical variable for the hypothesis test. A threshold for the hypothesis that the spectra are different was proposed. The Bayesian prior odds ratio was estimated from multiple spectra of the same sample. The posterior odds ratio was used to quantity the spectral similarity measure of the two spectra. Diffuse reflectance near-infrared spectra of tobacco samples of two formulations were used to demonstrate this method. The results show that this new method can detect subtle differences between the spectra.     

Bergman polynomials on an archipelago: Estimates, zeros and shape reconstruction

Growth estimates of complex orthogonal polynomials with respect to the area measure supported by a disjoint union of planar Jordan domains (called, in short, an archipelago) are obtained by a combination of methods of potential theory and rational approximation theory. The study of the asymptotic behavior of the roots of these polynomials reveals a surprisingly rich geometry, which reflects three characteristics: the relative position of an island in the archipelago, the analytic continuation picture of the Schwarz function of every individual boundary and the singular points of the exterior Green function. By way of explicit example, fine asymptotics are obtained for the lemniscate archipelago |z^m−1|<r^m, 0<r<1, which consists of m islands. The asymptotic analysis of the Christoffel functions associated to the same orthogonal polynomials leads to a very accurate reconstruction algorithm of the shape of the archipelago, knowing only finitely many of its power moments. This work naturally complements a 1969 study by H. Widom of Szegő orthogonal polynomials on an archipelago and the more recent asymptotic analysis of Bergman orthogonal polynomials unveiled by the last two authors and their collaborators.