关于条件信任函数

本文首先基于理论和实践两方面的考虑,给出了建立条件信任函数公式的准则;然后依据给定的准则.讨论了已有的几类条件信任函数公式的优点和弊病;最后我们给出了一种新的条件信任函数公式,其具备所期望的所有条件.同时为验证条件信任函数的性质的需要,我们还首次建立了几类有限集上信任函数的实例.     

摩擦市场条件下的双目标投资组合模型模糊优化

首先建立了摩擦市场条件下基于收益率分布偏度水平的双目标投资组合模型.在此基础上,将模糊集合的概念引入到该模型中,用模糊数学中的线性隶属函数处理了其中的风险目标和收益目标,建立了摩擦市场条件下基于收益率分布偏度水平的模糊型双目标投资组合模型.然后,针对该模型进行了新型遗传算法设计(动态遗传算法).最后用一个具体的算例给出了该模型的一个实例最优解,体现了多样化投资分散风险的组合投资原理.     

多目标优化正则条件的一个注记

给出带不等式约束的非光滑多目标优化问题正则条件的一个例子.通过该例,指出最近由Burachik和Rizvi利用线性化锥提出的可微多目标优化问题的正则条件不能利用Clarke导数推广到非光滑情形.     

一种多目标条件风险值数学模型

研究了一种多目标条件风险值(CVaR)数学模型理论.先定义了一种多目标损失函数下的α-VaR和α-CVaR值,给出了多目标CVaR最优化模型.然后证明了多目标意义下的α-VaR和α-CVaR值的等价定理,并且给出了对于多目标损失函数的条件风险值的一致性度量性质.最后,给出了多目标CVaR模型的近似求解模型.     

带概率条件的层次分析法(AHP)在车型组合决策中的应用

本文建立了车型组合决策所需要的层次结构模型 ,并运用文中所给出的带概率条件的对象层元素合权重排序公式对本文模型进行了求解     

几种基于CAPM的最优投资组合构造方案及其比较

本文在William Sharpe的资本资产定价模型（简称CAPM）的基础上,考虑了条件CAPM,就条件CAPM中的β系数为常数和时变系数两种情况,在不同的假设下分别给出了描述真实市场的模型,利用此模型给出了条件CAPM中模型参数的估计方法。对每种不同的描述真实市场的模型,我们选用了上海股市的若干股票构造了最优投资组合,并进行投资组合评估分析,最后对这几种情况下的最优投资组合的表现进行了比较。     

基于CVaR的最优投资组合模型算法分析

通过引入光滑因子,改进了基于条件风险值(CVaR)的最优投资组合线性模型,并详细介绍了以VaR最小为目标函数的最优投资组合模型的算法设计思想与过程.     

不确定条件下具有容差项的Markowitz证券组合投资模型的最优化解法

在分析证券市场中证券组合投资不确定性质的基础上,通过对Markowitz模型中证券期望收益与方差引入容差项来度量证券市场的不确定性,建立了不确定条件下具有容差项的Markowitz证券组合投资模型;分类讨论了容差的上界与下界所对应的两类有效组合前沿,得到了不确定条件下的证券组合投资模型的最优化解法及相关定理;最后给出了一个具体的数值实例．     

多部件系统故障预防工作的组合优化

研究了实践中常见的四种预防工作组合类型,即定时维修、功能检测、使用检查及检查与定时维修的组合策略,以单位时间维修费用最小为目标建立了多部件故障预防工作的组合优化模型.在此基础上,提出了两个故障预防工作的组合优化算法,并给出了计算示例以说明模型和算法的性能.     

n—集合函数多目标规划的最优性条件

本文在广义ρ－凸的条件下给出了ｎ集合函数多目标规划解的必要和充分条件。     

条件极值两种求法的不等价条件分析

本文说明了求条件极值的代入法与Ｌａｇｒａｎｇｅ乘数法的条件不等价。分析了这种不等价的原因，得到了求一般条件极值时，代入法与Ｌａｇｒａｎｇｅ乘数法均有效、前者无效而后者有效，以及两种方法均无效的各种不同条件．     

一类条件期望的计算(英文)

本文从条件期望的抽象定义出发给出一类条件期望的计算方法.作为应用,作者计算了文[1]中求条件期望的两个例子.经过比较发现,本文的方法要简单些.     

Conditional colorings of graphs

For an integer r>0, a conditional(k,r)-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex of degree at least r in G will be adjacent to vertices with at least r different colors. The smallest integer k for which a graph G has a conditional (k,r)-coloring is the rth order conditional chromatic number χ_r(G). In this paper, the behavior and bounds of conditional chromatic number of a graph G are investigated.     

On Conditional Independence,Mixing, and Association

Abstract

This is a follow-up to a recent article by Prakasa Rao [15 Prakasa Rao , B.L.S. 2008 . Conditional independence, conditional mixing and association . Annals of the Institute of Statistical Mathematics AISM , doi: 10.1007/S10463-007-0152-2 . [Google Scholar]] on conditional independence, conditional mixing and conditional association. The purpose of this article is to derive rigorously some results following from conditioning. To this end, a brief review is presented of the concepts of conditional independence of events, classes of events, and random variables, followed by a conditional version of a factorization theorem, as well as a first installment of some basic results. Next, the concepts of conditional covariance and variance are introduced, and a second installment of basic results follows. Furthermore, a certain representation of the covariance is established in detail, followed by a conditional version of it, as well as a generalization. The concept of the conditional characteristic function is also recalled, and a certain inequality is established. Finally, the concept of conditional positive (negative) quadrant dependence, as well as that of conditional positive (negative) association are introduced. The article concludes with the derivation of the conditional versions of some known results, regarding positive (negative) association. This is done anticipating that conditional association (and also conditional mixing) will prove to be of significant applicability.     

Conditional versions of limit theorems for conditionally associated random variables

Relation between association and conditional association is answered, several examples show that the association of random variables does not imply the conditional association, and vice versa. Several fundamental properties of conditional associated random variables are developed, which extend the corresponding ones under the non-conditioning setup. By means of these properties, some conditional Hájek-Rényi type inequalities, a conditional strong law of large numbers and a conditional central limit theorem stated in terms of conditional characteristic functions are established, which are conditional versions of the earlier results for associated random variables, respectively. In addition, some lemmas in the context are of independent interest.     

求条件极值的一种新方法

利用线性代数的理论方法，对多元函数求条件极值的拉格朗日乘数法加以改进，建立了求条件极值的一种新方法     

Conditional tests for elliptical symmetry

In this paper, we suggest the conditional test procedures for testing elliptical symmetry of multivariate distribution. The conditional tests are exactly valid if the symmetric center and the shape matrix are given and are asymptotically valid if they are unknowns to be estimated. The equivalence, in the large sample sense, between the conditional tests and their unconditional counterparts is established. The power behavior of the tests under global as well as local alternatives is investigated theoretically. A small simulation study is performed.     

双变量参数联合函数的条件均值和条件方差(英文)

联合函数是指连接单变量边际分布的多变量函数.联合函数由Sklar(1959)在概率测度空间的内容时引入的.本文主要对边际分布是标准正态分布函数U(0,1)的Farlie-Gum-bel-Morgenstern和Gumbel-Hougaard这两个双变量参数联合函数进行研究,我们得到了他们密度函数的基本性质并导出了他们的条件均值和条件方差.另外,本文还给出了不同参数的条件均值和条件方差的相应图示,并进行了对比和解释.     

Conditional Stability Estimates for Ill-Posed PDE Problems by Using Interpolation

The focus of this article is on conditional stability estimates for ill-posed inverse problems in partial differential equations. Conditional stability estimates have been obtained in related literature by a couple different methods. In this article, we propose a method called interpolation method, which is based on interpolation in variable Hilbert scales. We provide the theoretical background of this method and show that optimal conditional stability estimates are obtained. The capabilities of our method are illustrated by a comprehensive collection of different inverse and ill-posed PDE problems containing elliptic and parabolic problems, one source problem and the problem of analytic continuation.     

Conditional expectation and the Bergman projection

For any σ-algebra of measurable subsets of the unit disk generated by a finite Blaschke product, we prove that the associated conditional expectation operator commutes with the Bergman projection operator if and only if the σ-algebra is generated by a monomial. In the process, a formula for the conditional expectation operator (under certain assumptions) is obtained. When compared with earlier results of A.B. Aleksandrov concerning conditional expectation associated with σ-algebras of measurable subsets of the circle, our results exhibit a stark contrast between the way conditional expectation operators act in the Bergman and Hardy space settings.