市场低迷时期证券投资风险的度量

当股票市场处于疲软状态，即通常所说的熊市时，证券投资风险的评估和规避就显得尤为重要。本从保险中的破产理论出发，运用复合泊松过程的方法，在一个事例的基础上，提出一种当市场比较疲软时在短期内评估投资风险的方法，并以2002年9月2日到2002年12月31日这79个交易日中具有代表性的一支股票——深发展(000001)为例，进行了模型的求解和分析，并在此基础上提出了几套改进模型的方案和本方法的扩展应用。     

证券投资组合理论的一种新模型及其应用

马科维茨(Markowitz)以证券收益率的方差作为投资风险的测度建立了组合证券投资模型，本基于熵的概念，在研究马科维茨(Markowitz)证券投资组合模型的基础上，分析了该模型用方差度量风险的不足，进而提出一种新的证券投资组合优化模型，并以实例作了说明。     

随机双曲折现下的消费与最优投资策略探究

在本文中,我们主要讨论在随机双曲折现中,当投资者的消费行为是一个布朗运动时,其用于投资风险资产的最优投资额.基于汉密尔顿-雅克比-贝尔曼方程计算常数绝对风险厌恶型投资者的效用函数下的最优投资组合,并给出这组方程的近似解.在此基础上,我们分析当消费服从Wiener过程时风险资产投资的一些重要性质,研究消费行为与风险资产投资行为之间的关系.     

CVaR风险度量模型在投资组合中的运用

风险价值(VaR)是近年来金融机构广泛运用的风险度量指标，条件风险价值(CVaR)是VaR的修正模型，也称为平均超额损失或尾部VaR，它比VaR具有更好的性质。在本中，我们将运用风险度量指标VaR和CVaR，提出一个新的最优投资组合模型。介绍了模型的算法，而且利用我国的股票市场进行了实证分析，验证了新模型的有效性，为制定合理的投资组合提供了一种新思路。     

选择资产组合的EP-MV模型及最优解的解析表示

本文提出了存在无风险资产贷出或借入时的有效投资组合模型(EP-MV模型)，研究了不允许卖空(投资比例非负)约束条件下，EP-MV优化模型的算法，给出了有效投资组合投资比例的解析表示．在资产收益由多因素模型产生的基础上，得到了资产与有效投资组合的期望收益及风险的估计，便于实际应用．     

一种工程软件可靠性评估方法

本文在分析多种软件可靠性模型的基础上，提出一种综合“Ｎａｓｌｏｎ模型”与“硬－软件复合系统结构模型”二者优点的软件可靠性评估方法，本方法简单，可行，对其它领域的软件可靠性评估有一定参考价值。     

风险条件下基于收益视角的最优投资决策研究

给出了风险条件下基于收益视角的损失最小化投资组合模型.数值试验表明,当投资者预期收益较高时,该模型等价于条件在险价值模型,当投资者满足于较低收益时,该模型优于条件在险价值模型.提出的基于主成分分析的情景生成方法避免了过度分散投资,投资组合模型的最优目标值随情景数目的增加快速趋于收敛;该情景生成方法无需假定随机收益的分布,融合了收益分布的非对称及尖峰等统计特征,主成分分析法的降维优势使该方法也适合于资产数目较大时的情景生成.     

基于POET方法的投资组合选择模型

Markowitz开创了现代投资组合理论的先河,他提出的均值方差模型为后来投资组合选择模型的研究奠定了基础.然而,许多学者的研究表明,均值方差模型对参数非常敏感,当模型参数的估计存在较大的误差时,模型并不是在配置风险和收益,而是在配置误差.模型的误差分别来自收益端和风险端,为了改善收益端的参数估计,学者们提出了更具有实际应用价值的Black-Litterman模型,而如何改善风险端的估计误差还有待进一步的研究.在实际应用中,有效的数据样本往往较少,当资产数量较大时,样本协方差矩阵存在很大的估计误差,因此,引入POET方法估计协方差矩阵提高协方差矩阵的估计精度,从风险端改善投资组合选择模型的配置效率.将构建的投资组合选择模型分别应用在申万一级行业指数和二级行业指数上,算例分析的结果表明,引入POET方法后模型有更好的表现.     

开放式基金流动性赎回风险实证分析与评价

本基于Vikram Nanda，M．P．Narayanan(2000)的基金管理能力与流动性需求、流动性赎回风险关系模型的修正，研究结果表明，基金管理所预期的利润与其管理能力正相关，而与流动性成本和流动性需求的风险呈负相关；负担基金管理的边际能力相对于低流动性需求投资的数量和高流动性需求投资的风险而言是递减的；最低赎回费用与高流动性需求投资的风险和低流动性需求投资的相对稀缺性正相关。在此基础上对我国开放式基金的流动性赎回风险进行实证分析评价，并提出了几点政策建议。     

目标规划法在证券组合投资中的应用

证券投资是目前我国经济中的一大热点。本以Markowitz证券组合投资理论为基础，运用目标规划的方法建立一种新的证券组合投资决策模型。在本模型中综合考虑了证券组合的收益，风险，交易费用等因素，对投资选择有效证券组合有一定的实用价值。     

Estimation of the number of components of finite mixtures of multivariate distributions

An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.     

Eigenvector p-Bases of Rings of Constants of Derivations

Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing A^p.     

Galois Structure of K-Groups of Rings of Integers

N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.     

有资格限制的指派问题的求解方法

在实际的指派工作中，常会遇到某个人有没有资格去承担某项工作的问题，因此，本建立了有资格限制的指派问题的数学模型。在此数学模型中，将效益矩阵转化为判定矩阵，由此给出了判定此种指派问题是否有解的方法；在有解的情况下，进一步将效益矩阵转化为求解矩阵，从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。     

On Sums of Coefficients of Products of Polynomials

We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings.     

Convergence of sequences of sets of associated primes

It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.

     

Rates of Convergence of Means of Euclidean Functionals

Let L be the Euclidean functional with p-th power-weighted edges. Examples include the sum of the p-th power-weighted lengths of the edges in minimal spanning trees, traveling salesman tours, and minimal matchings. Motivated by the works of Steele, Redmond and Yukich (Ann. Appl. Probab. 4, 1057–1073, 1994, Stoch. Process. Appl. 61, 289–304, 1996) have shown that for n i.i.d. sample points {X ₁,…,X _n } from [0,1] ^d , L({X ₁,…,X _n })/n ^(d−p)/d converges a.s. to a finite constant. Here we bound the rate of convergence of EL({X ₁,…,X _n })/n ^(d−p)/d . Y. Koo supported by the BK21 project of the Department of Mathematics, Sungkyunkwan University. S. Lee supported by the BK21 project of the Department of Mathematics, Yonsei University.     

Number of connected components of groups of real points of adjoint groups

We present a unified approach to compute the number of connected components in the group of real points of adjoint almost simple real algebraic groups.     

Enumeration of perfect matchings of a type of Cartesian products of graphs

Let G be a graph and let Pm(G) denote the number of perfect matchings of G.We denote the path with m vertices by P_m and the Cartesian product of graphs G and H by G×H. In this paper, as the continuance of our paper [W. Yan, F. Zhang, Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians, Adv. Appl. Math. 32 (2004) 175-188], we enumerate perfect matchings in a type of Cartesian products of graphs by the Pfaffian method, which was discovered by Kasteleyn. Here are some of our results:1. Let T be a tree and let C_n denote the cycle with n vertices. Then Pm(C₄×T)=∏(2+α²), where the product ranges over all eigenvalues α of T. Moreover, we prove that Pm(C₄×T) is always a square or double a square.2. Let T be a tree. Then Pm(P₄×T)=∏(1+3α²+α⁴), where the product ranges over all non-negative eigenvalues α of T.3. Let T be a tree with a perfect matching. Then Pm(P₃×T)=∏(2+α²), where the product ranges over all positive eigenvalues α of T. Moreover, we prove that Pm(C₄×T)=[Pm(P₃×T)]².