多元时间序列模型协方差矩阵的递归算法

本文推导了多元时序模型的协方差矩阵与模型参数的关系式，并给出了计算多维时序过程自协方差矩阵的递归算法     

多元时间序列模型协方差矩阵的递归算法

本推导了多元时序横型的协方差矩阵与模型参数的关系式，并给出了计算多维时序过程自协方差矩阵的递归算法。     

多元随机变量的某些问题

本文讨论多元随机变量之期望向量、协方差矩阵与边际分布、条件分布的期望向量、协方差矩阵之间的关系.还讨论了多元随机变量服从多元正态分布的某个充分条件.     

矩阵损失函数下回归系数矩阵的非齐次线性估计的可容许性

在二次矩阵损失函数下研究了协方差矩阵未知的多元线性模型中回归系数矩阵的可估线性函数的矩阵非齐次线性估计的可容许性,给出了矩阵非齐次线性估计在线性估计类中可容许的一个充要条件.     

一类多元重复测量模型参数的似然比检验及其功效分析

在多元重复测量试验模型下,当受试对象观测矩阵的协方差矩阵∑为等方差等协方差结构时,给出了参数的似然比检验统计量.给出该检验在原假设下的渐近零分布和在备择假设下的渐近非零分布,并就检验的功效进行了分析.     

多元线性模型中条件最优预测的稳健性

研究了多元线性模型中条件最优线性无偏预测的稳健性问题,得到了条件线性可预测变量的这种预测关于协方差矩阵具有稳健性的充要条件.     

多元线性回归中度量影响的置信域体积比统计量

本文从多元线性回归模型回归系数的椭球置信域出发,导出度量影响的置信域体积比诊断统计量,并给出了它在协方差矩阵未知时的近似表达式。     

关于链模型的回归系数与协方差阵元素的关系

该文以数学公式的形式严格定义了[1][2]提出的多元链回归模型,块回归链模型．导出了这两类模型的回归系数用协方差矩阵元素表式的解析表达式。这些都去掉了[1][2]要求正态分布的假设．它们对图模型的理论研究及其应用都是很有价值的。最后本文还对一种块链模型讨论了它的回归系数与协方差阵元素所满足约束的互相对应关系．     

基于因子收缩方法的高维协方差估计

高维协方差矩阵在经济、金融、生物等众多领域中有着广泛应用.基于收缩估计模型,构造样本协方差矩阵与因子模型协方差矩阵的凸线性组合,通过对因子模型的改进来提高模型估计精度.在构造因子模型时,引入因子选择准则(pc_p3(k))来确定因子个数:在确定最优权重α时,使用基于MSE(S)分解的思想求解.通过数据验证发现,相较于传统方法,提升了协方差矩阵估计精确性;在构造投资组合模型时,也可以有效降低投资风险.     

多元线性模型中回归系数矩阵非齐次线性估计的可容许性

该文研究了协方差矩阵未知的多元线性模型中,二次矩阵损失函数下回归系数矩阵可估线性函数的非齐次线性估计的可容许性.不需正态分布的假设,作者给出矩阵非齐次线性估计在线性估计类中可容许的充要条件;在正态分布的假设下,作者给出矩阵非齐次线性估计在一切估计组成的估计类中可容许的充分条件.     

Existence of magic 3‐dimensional rectangles

Since the complete solution for the existence of magic 2‐dimensional rectangles in 1881, much attention has been paid on the existence of magic l‐dimensional rectangles for . The existence problem for magic l‐dimensional rectangles with even sizes has been solved completely for all integers . However, very little is known for the existence of magic l‐dimensional rectangles () with odd sizes except for some families and a few sporadic examples. In this paper, we focus our attention on the existence of magic 3‐dimensional rectangles and prove that the necessary conditions for the existence of magic 3‐dimensional rectangles are also sufficient. Our construction method is mainly based on a new concept, symmetric zero‐sum subset partition, which plays a crucial role in the recursive constructions of magic 3‐rectangles similar to that of PBD in the PBD‐closure construction in combinatorial design theory.     

Crisis and risk dependencies

The knowledge of the multivariate stochastic dependence between the returns of asset classes is of importance for many finance applications, such as asset allocation or risk management. By means of goodness-of-fit tests, we analyze for a multitude of portfolios consisting of different asset classes whether the stochastic dependence between the portfolios’ constituents can be adequately described by multivariate versions of some standard parametric copula functions. Furthermore, we test whether the stochastic dependence between the returns of different asset classes has changed during the recent financial crisis. The main findings are: First, whether a specific copula assumption can be rejected or not, crucially depends on the asset class and the time period considered. Second, different goodness-of-fit tests for copulas can yield very different results and these differences can vary for different asset classes and for different tested copulas. Third, even when using various goodness-of-fit tests for copulas, it is not always possible to differentiate between various copula assumptions. Fourth, during the financial crisis, copula assumptions are more frequently rejected. However, the results also raise some concerns over the suitability of goodness-of-fit tests for copulas as a diagnostic tool for identifying stressed risk dependencies.     

An Improved Binomial Lattice Method for Multi‐Dimensional Options

A binomial lattice approach is proposed for valuing options whose payoff depends on multiple state variables following correlated geometric Brownian processes. The proposed approach relies on two simple ideas: a log‐transformation of the underlying processes, which is step by step consistent with the continuous‐time diffusions, and a change of basis of the asset span, to transform asset prices into uncorrelated processes. An additional transformation is applied to approximate driftless dynamics. Even if these features are simple and straightforward to implement, it is shown that they significantly improve the efficiency of the multi‐dimensional binomial algorithm. A thorough test of efficiency is provided compared with most popular binomial and trinomial lattice approaches for multi‐dimensional diffusions. Although the order of convergence is the same for all lattice approaches, the proposed method shows improved efficiency.     

On singularities of solution of Maxwell's equations in axisymmetric domains with conical points

Boundary value problems (BVP) in three‐dimensional axisymmetric domains can be treated more efficiently by partial Fourier analysis. Partial Fourier analysis is applied to time‐harmonic Maxwell's equations in three‐dimensional axisymmetric domains with conical points on the rotation axis thereby reducing the three dimensional BVP to an infinite sequence of 2D BVPs on the plane meridian domain Ω_a?? of . The regularity of the solutions u _n (n∈?₀:={0, 1, 2,…}) of the two dimensional BVPs is investigated and it is proved that the asymptotic behaviour of the solutions u _n near an angular point on the rotation axis can be characterized by singularity functions related to the solutions of some associated Legendre equations. By means of numerical experiments, it is shown that the solutions u _n for n∈?₀\{1} belong to the Sobolev space H² irrespective of the size of the solid angle at the conical point. However, the regularity of the coefficient u ₁ depends on the size of the solid angle at the conical point. The singular solutions of the three dimensional BVP are obtained by Fourier synthesis. Copyright © 2006 John Wiley & Sons, Ltd.     

Partial differential integral equation model for pricing American option under multi state regime switching with jumps

In this paper, we consider a two dimensional partial differential integral equation (PDIE) model for pricing American option. A nonlinear rationality parameter function for two asset problems is introduced to deal with the free boundary. The rationality parameter function is added in the PDIEs used for pricing American option problems under multi-state regime switching with jumps. The resulting two dimensional nonlinear system of PDIE is then numerically solved. Based on real poles rational approximation, a strongly stable highly efficient and reliable method is developed to solve such complicated systems of PIDEs. The method is build in a predictor corrector style which makes it linearly implicit, therefore, avoids solving nonlinear systems of equations at each time step in all regimes. The method is seen to maintain the stability and convergence for large jump sizes and high volatility in each regime. The impact of regime switching on option prices corresponding to different values interest rate, volatility, and rationality parameter is computed, illustrated by graphs and given in the tables. Convergence results in each regime are presented and time evolution graphs are given to show the effectiveness and reliability of the method.     

Sections of the regular simplex – Volume formulas and estimates

We state a general formula to compute the volume of the intersection of the regular n‐simplex with some k‐dimensional subspace. It is known that for central hyperplanes the one through the centroid containing vertices gives the maximal volume. We show that, for fixed small distances of a hyperplane to the centroid, the hyperplane containing vertices is still volume maximizing. The proof also yields a new and short argument for the result on central sections. With the same technique we give a partial result for the minimal central hyperplane section. Finally, we obtain a bound for k‐dimensional sections.     

On data depth in infinite dimensional spaces

The concept of data depth leads to a center-outward ordering of multivariate data, and it has been effectively used for developing various data analytic tools. While different notions of depth were originally developed for finite dimensional data, there have been some recent attempts to develop depth functions for data in infinite dimensional spaces. In this paper, we consider some notions of depth in infinite dimensional spaces and study their properties under various stochastic models. Our analysis shows that some of the depth functions available in the literature have degenerate behaviour for some commonly used probability distributions in infinite dimensional spaces of sequences and functions. As a consequence, they are not very useful for the analysis of data satisfying such infinite dimensional probability models. However, some modified versions of those depth functions as well as an infinite dimensional extension of the spatial depth do not suffer from such degeneracy and can be conveniently used for analyzing infinite dimensional data.     

A short overview of some behavioural scenarios for derivative pricing in incomplete markets

We shortly describe three different but related scenarios for determination of asset prices in an incomplete market: one scenario uses a market game approach whereas the other two are based on risk sharing or regret minimizing considerations. Furthermore, we point out some new dynamical schemes modeling the convergence of the buyer's and of the seller's prices of a given asset to a unique price. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Some infinite families of 2‐designs from PG (n,q)

In this paper, we establish the existence of some infinite families of 2‐designs from ‐dimensional projective geometry , which admit ‐dimensional projective special linear group as their flag‐transitive automorphism group.     

Fast solution algorithms for exponentially tempered fractional diffusion equations

In this article, a fast‐iterative method and a fast‐direct method is proposed for solving one‐dimensional and two‐dimensional tempered fractional diffusion equations with constant coefficients. The proposed iterative method is accelerated by circulant preconditioning which is shown to converge superlinearly while the proposed direct method is based on circulant and skew‐circulant representation for Toeplitz matrix inversion. In one‐dimensional case, the operation cost of the proposed methods are both shown to be with memory requirement in each time step, where is the number of spatial nodes. With the alternating direction implicit method, it is proven that the proposed fast solution algorithms can be extended to handle two‐dimensional tempered fractional diffusion equations with operation cost and memory requirement in each time step, where the number of spatial nodes in ‐direction and ‐direction both equal to . Numerical examples are provided to illustrate the effectiveness and efficiency of the proposed methods.