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.     

多周期多目标条件风险值模型

在商业、工业、电力和房地产等行业中存在许多复杂的多周期风险决策问题,它的数学模型研究对于解决这些问题具有重要的作用.作者建立了一种新的多周期多目标条件风险值(CVaR)数学模型理论和方法.先定义了一种带时间段的多周期多目标损失函数下的α-VaR和α-CVaR值,给出了一类多周期多目标CVaR最优化模型.然后,证明了多目标意义下的对应模型的等价定理,给出了多周期多目标CVaR模型的近似求解等价模型.最后,建立了一种生产企业在供过于求和供不应求两种情形下产生的多周期双目标CVaR模型,针对一个电力生产企业进行的数值实验,表明了模型可以得到在最小供给的用电损失分布下的各周期下的相匹配供电策略,可以帮助供电部门各个时期供电不平衡状况下的风险控制.     

多目标条件风险值的一种近似求解方法

本文研究了一种求解多目标条件风险值问题的近似方法,首先引入了多个损失函数在对应的置信水平下关于一个证券组合的α-VaR损失值,以及α-CVaR损失值概念．α-CVaR损失值表明了在给定的证券组合于置信水平对应的最小信用风险值的条件期望损失值,那么求出这样的最小条件期望损失值的模型构成了一个求解α-CVaR损失值的多目标问题,它的解就是最小条件期望损失值的有效证券组合,即Pareto弱有效解．为了求解它的Pareto弱有效解,我们引进了损失函数对应的优化问题(SCVaR),可以通过求解非线性规划问题(SCVaR)的最优解近似地刻画α—CVaR损失值,这样使得求解α-CVaR损失值变得容易．     

求解带有交易费的CVaR投资组合模型的L-S算法

本文假设投资者是风险厌恶型,用CVaR作为测量投资组合风险的方法.在预算约束的条件下,以最小化CVaR为目标函数,建立了带有交易费用的投资组合模型.将模型转化为两阶段补偿随机优化模型,构造了求解模型的随机L-S算法.为了验证算法的有效性,用中国证券市场中的股票进行数值试验,得到了最优投资组合、VaR和CVaR的值.而且对比分析了有交易费和没有交易费的最优投资组合的不同,给出了相应的有效前沿.     

多目标条件风险值问题的等价定理

条件风险值问题是研究信用风险最优化的一种新的模型，本文研究了一类多目标条件风险值问题等价定理，我们引入了多个损失函数在对应的置信水平下关于一个证券组合的α-VaR损失值(最小信用风险值)和α-CVaR损失值(最小信用风险值对应的条件期望损失值或条件风险价值度量)概念，为了求得α-CVaR损失值下的弱：Pareto有效解，我们证明了它等价于求解另一个多目标规划问题的Pateto有效解，这样使得问题的求解变得简单．     

基于CVaR投资组合优化问题的光滑化方法

对选定的风险资产进行组合投资,以条件风险价值(CVaR)作为度量风险的工具,建立单期投资组合优化问题的CVaR模型。目标函数中含有多重积分与plus函数,产生情景矩阵将多重积分计算转化成求和运算,提出plus函数的一个新的一致光滑逼近函数并给出求解CVaR模型的光滑化方法,最后的实证研究表明了本文算法的优越性。     

基于Pair-Copula-GARCH模型与CVaR的时变投资组合优化

以过去的信息为条件,以一致性风险度量CVaR为优化目标,以组合收益率为约束条件,建立了时变投资组合优化模型,通过基于pair-copula-GARCH模型的蒙特卡洛模拟方法得到未来某时刻收益率的多个可能情景,并引入一个特殊函数实现了投资组合模型的线性化,得到了最优投资组合策略.最后针对提出的模型进行了实例分析.     

区间证券多目标投资组合的β模型

基于区间证券组合的系统风险与非系统风险问题,建立一种新的含β约束的区间证券投资组合的多目标优化模型,使得证券组合投资更具柔性,最后,结合实例分析了该模型的现实应用价值.     

含MCVaR的投资组合优化统一模型

研究了Duarte提出的投资组合优化统一模型及条件风险价值(CVaR),分析了以CVaR为风险度量的投资组合优化模型的具体形式,建立了统一七种模型的投资组合优化统一模型,并发现统一模型是一个凸二次规划问题.     

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.     

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP ——In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.     

Boundedness for commutators of multipliers on Hardy type spaces

In this paper, we study the commutators generalized by multipliers and a BMO function. Under some assumptions, we establish its boundedness properties from certain atomic Hardy space Hb^p（R^n） into the Lebesgue space L^p with p 〈 1.     

A unified approach to certain problems of best local approximation

In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables. Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.     

Towards Excellence in Science Chinese Academy of Sciences

<正>May 26,2014,Beijing Science is a human enterprise in the pursuit of knowledge.The scientific revolution that occurred in the 17th Century initiated the advances of modern science.The scientific knowledge system created by     

THE 8~(th) INTERNATIONAL CONGRESS ON INDUSTRIAL AND APPLIED MATHEMATICS

<正>August 10-14,2015Beijing,ChinaThe International Congress on Industrial and Applied Mathematics(ICIAM)is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics.From August 10 to 14,2015,mathematicians,scientists     

Bounds for the zeros of polynomials

Let P(z)=∑↓j=0↑n ajx^j be a polynomial of degree n. In this paper we prove a more general result which interalia improves upon the bounds of a class of polynomials. We also prove a result which includes some extensions and generalizations of Enestrǒm-Kakeya theorem.     

Boundedness of commutators related to Marcinkiewicz integrals on hardy type spaces

In this paper, the authors study the boundedness of the operator [μΩ, b], the commutator generated by a function b ∈ Lipβ(Rn)(0 ＜β≤ 1) and the Marcinkiewicz integrals μΩ, on the classical Hardy spaces and the Herz-type Hardy spaces in the case Ω∈ Lipα(Sn-1)(0 ＜α≤ 1).     

Generalization of the interaction between Haar approximation and polynomial operators to higher order methods

In applications it is useful to compute the local average empirical statistics on u. A very simple relation exists when of a function f（u） of an input u from the local averages are given by a Haar approximation. The question is to know if it holds for higher order approximation methods. To do so, it is necessary to use approximate product operators defined over linear approximation spaces. These products are characterized by a Strang and Fix like condition. An explicit construction of these product operators is exhibited for piecewise polynomial functions, using Hermite interpolation. The averaging relation which holds for the Haar approximation is then recovered when the product is defined by a two point Hermite interpolation.     

Jacobi polynomials used to invert the laplace transform

Given the Laplace transform F(s) of a function f(t), we develop a new algorithm to find an approximation to f(t) by the use of the classical Jacobi polynomials. The main contribution of our work is the development of a new and very effective method to determine the coefficients in the finite series expansion that approximation f(t) in terms of Jacobi polynomials. Some numerical examples are illustrated.