投资组合模型的线性分式规划解法

本文对证券投资组合的最大收益、最小风险投资决策问题,提出了一个兼顾收益和风险的效用函数;并建立了基于线性分式规划的投资组合选择模型,给出了该模型的线性分式规划解法。     

风险投资组合的线性规划模型的建立及求解

当要对比市场上的无风险投资(如存入银行)与多种风险投资组合两种投资方式并进行组合投资策略时,要考虑两个目标,即尽可能获得最大总收益同时承担尽可能小的总体风险,但是这两个目标很难同时实现,因为高收益意味着高风险.文章通过设计一个有关于投资组合的线性规划模型来讨论这两个问题.通过选取合适的决策变量以化解风险函数的非线性性.通过对因子进行加权,我们求得了最佳方案并得到了有效投资曲线.投资者根据有效的投资曲线结合自己的偏好,选择自己的投资方向.最后通过非线性规划,说明线性规划的结果对于交易费收取的阈值有一定的容忍度.     

项目投资组合收益与风险计量

项目投资获取收益的同时也蕴含着风险,通常收益和风险成正比.因此,面对众多的投资项目,投资公司的重要决策就是选择合理的项目组合和投资比例以满足其收益和风险偏好.盈亏平衡分析、敏感性分析和概率分析可以描述单项目投资的风险因素对收益的影响,但是不同项目的风险分析结果不能累加,使得项目组合的风险难以计量.本文将证券投资组合理论应用于实体项目投资组合,建立基于均值-方差分析的项目组合风险计量模型.     

风险投资非系统风险模糊综合评判

由于风险投资中的系统风险一般是不能由分散投资来降低的,故本文仅对风险投资的非系统风险进行了分析,建立了全面的非系统风险评价指标,利用属性层次模型(AHM)法给出了指标的重要性权重,再利用适合风险投资特点的模糊综合评价方法对其进行综合评判.最后,以实例说明了此方法的可行性.     

基于遗传算法的单位风险收益最大投资组合模型研究

文章根据中国证券市场的实际要求,考虑了交易费用、交易量以及最大投资上限等实际因素,以投资组合的收益为分子,以投资组合的风险价值为分母,建立了一个单位风险收益最大投资组合的非线性整数规划模型,给出了该模型的基于整数编码的遗传算法.实证分析表明,该模型是合理的并且给出的算法是有效的.     

降低创业家道德风险的分阶段投资分析

文章从降低风险投资风险,提高风险投资公司收益角度出发,选取风险资本分阶段投资的投资决策作为研究视角,研究分阶段投资的运作机制,从而为我国风险投资实践提供指导.     

风险投资基金的风险分析与决策

风险投资基金具有很高的投资风险,由于它的投资对象在技术和市场方面都具有很大的不确定性,因而投资失败的可能性很大.一般而言,风险与收益呈正相关关系,风险越大,预期收益越大.从某种程度上讲,消除风险就等于肖除收益.风险本身并不是坏东西,关键是如何管理好风险.风险管理的目的就是在防范和控制风险的情况下,实现收益最大化.     

信用衍生产品在风险管理中的应用

一、现代信用风险的几个特征 信用风险有其传统意义和现代意义上的区别,传统意义上的信用风险是指借款人不能按期还本付息而给贷款人造成损失的风险,造成的损失一般被理解为只有当违约实际发生时才会产生,因此,信用风险又称为违约风险;现代意义的风险是指包括由交易对手直接违约和交易对手违约可能性变化而给投资组合造成损失的风险,区别于传统意义的信用风险,现代意义的信用风险采取盯市的方法,从现代组合投资理论的角度出发,投资者的投资组合不仅会因交易对手的直接违约而损失,而且会因交易对手履约可能性的变化影响组合投资损失的大小,所以现代意义上的信用风险应包括交易对手直接违约和交易对手违约可能性变化两个方面,这样因信用水平的下降或者履约能力的变化而使投资组合中资产价格下降进而造成损失的风险,显然它也是一种市场风险,因此现代意义上的信用风险与市场风险有重叠的部分.     

不允许卖空条件下组合证券投资的几个问题

现代组合证券投资理论研究不确定情形下理性投资行为的优化问题。1952年，H．M．MarkowttZ提出均值--方差模型（简称EVW，率先探讨了将现代证券理论应用到投资领域的可能性。马氏认为，一般投资者在选择证券时，同时存在希求满足和厌恶风险的倾向，最终的选择是在期望效用达到最大的目标下二者权衡的结果。对一含有n种风险证券的组合投资问题，记R--n种风险证券的收益列向量小--n种风险证券的期望收益列向量，已一收益的协方差矩阵，en--单位列向量，X--组合证券投资比例系数列向量，E--期望组合收益标量，V--组合收益方差标量，则EVM…     

实物期权与风险资本的阶段融投资制度安排

问题的提出 风险资本是在技术创新和金融创新相互作用过程中逐步形成的一种创新资本形态,其独创的运作机制和治理结构特别适合于高新技术产业的发展.与一般资本投资相比,风险资本的一个重要不同点就是其多阶段投融资制度安排.在美国,有限合伙人向风险投资基金注资一般是分期进行的,通常是在合同签字后立即投入其承诺资金的25%35%,然后在规定的时间按规定的数额分期投入余下金额,但是,有限合伙人也有权根据实际情况拒绝履行后期资金投入,违反合同的代价是被一般合伙人降低其在风险投资基金中已经取得的股份份额;同样,风险资本家在向创业企业投资时,也是分阶段投入的,根据创业企业成长状况,风险资本家不断追加其扩张所需的资本,但每一次投资都只是提供企业达到下一阶段所必须的资金量,并保留在下一阶段放弃投资的权利.按照Sahlman(1990)的估计,美国有限合伙公司对每一个项目的投资次数平均为3.     

A comparison of the classical and the linear programming approaches to the classification problem in discriminant analysis

Several mathematical programming approaches to the classification problem in discriminant analysis have recently been introduced. This paper empirically compares these newly introduced classification techniques with Fisher's linear discriminant analysis (FLDA), quadratic discriminant analysis (QDA), logit analysis, and several rank-based procedures for a variety of symmetric and skewed distributions. The percent of correctly classified observations by each procedure in a holdout sample indicate that while under some experimental conditions the linear programming approaches compete well with the classical procedures, overall, however, their performance lags behind that of the classical procedures.     

Continuity of f-projections and applications to the iterative proportional fitting procedure*

This paper proves continuity of f-projections and the continuous dependence of the limit matrix of the iterative proportional fitting procedure (IPF procedure) on the given matrix as well as the given marginals under certain regularity constraints. For finite spaces, the concept of f-projections of finite measures on a compact and convex set is introduced and continuity of f-projections is proven. This result is applied to the IPF procedure. Given a nonnegative matrix as well as row and column marginals the IPF procedure generates a sequence of matrices, called the IPF sequence, by alternately fitting rows and columns to match their respective marginals. The procedure is equivalent to cyclic f-projections. If the IPF sequence converges, the application of the continuity of f-projections yields the continuous dependence of the limit matrix on the given matrix. By generalized convex programming and under some constraints, it is shown that the limit matrix of the IPF sequence continuously depends not only on the given matrix but also on the marginals.     

Discussion on the paper by Stone

Summary. The single-input case of the 'technical efficiency' theory of M. J. Farrell is reformulated geometrically and algebraically. Its linear programming developments as 'data envelopment analysis' are critically reviewed, as are the related techniques of 'stochastic frontier analysis'. The sense and realism of using data envelopment analysis or stochastic frontier analysis techniques, rather than some value-based method, for the assessment of police force efficiency are questioned with reference to the Spottiswoode report and related studies.     

A quadratic programming approach to the construction of simultaneous confidence intervals

Richmond (1982) uses a linear programming approach to the construction of simultaneous confidence intervals for a set of linear estimable parametric functions of the normal mean vector. We present a quadratic programming approach which constructs narrower confidence intervals than the linear programming approach given by Richmond (1982).     

An Optimal Multivariate Stratified Sampling Design Using Dynamic Programming

Numerous optimization problems arise in survey designs. The problem of obtaining an optimal (or near optimal) sampling design can be formulated and solved as a mathematical programming problem. In multivariate stratified sample surveys usually it is not possible to use the individual optimum allocations for sample sizes to various strata for one reason or another. In such situations some criterion is needed to work out an allocation which is optimum for all characteristics in some sense. Such an allocation may be called an optimum compromise allocation. This paper examines the problem of determining an optimum compromise allocation in multivariate stratified random sampling, when the population means of several characteristics are to be estimated. Formulating the problem of allocation as an all integer nonlinear programming problem, the paper develops a solution procedure using a dynamic programming technique. The compromise allocation discussed is optimal in the sense that it minimizes a weighted sum of the sampling variances of the estimates of the population means of various characteristics under study. A numerical example illustrates the solution procedure and shows how it compares with Cochran's average allocation and proportional allocation.     

Optimal progressive interval censoring plan under accelerated life test with limited budget

In this paper, we investigate some inference and design problems related to multiple constant-stress accelerated life test with progressive type-I interval censoring. A Weibull lifetime distribution at each stress-level combination is considered. The scale parameter of Weibull distribution is assumed to be a log-linear function of stresses. We obtain the estimates of the unknown parameters through the method of maximum likelihood, and also derive the Fisher's information matrix. The optimal number of test units, number of inspections, and length of the inspection interval are determined under D-optimality, T-optimality, and E-optimality criteria with cost constraint. An algorithm based on nonlinear mixed-integer programming is proposed to the optimal solution. The sensitivity of the optimal solution to changes in the values of the different parameters is studied.     

An F Approximation to the Distribution of a Linear Combination of Chi-squared Variables.

A three-parameter F approximation to the distribution of a positive linear combination of central chi-squared variables is described. It is about as easy to implement as the Satterthwaite-Welsh and Hall-Buckley-Eagleson approximations. Some reassuring properties of the F approximation are derived, and numerical results are presented. The numerical results indicate that the new approximation is superior to the Satterthwaite approximation and, for some purposes, better than the Hall-Buckley-Eagleson approximation. It is not quite as good as the Gamma-Weibull approximation due to Solomon and Stephens, but is easier to implement because iterative methods are not required.     

On the Problem of Compromise Allocation in Multi-Response Stratified Sample Surveys

In stratified sample surveys, the problem of determining the optimum allocation is well known due to articles published in 1923 by Tschuprow and in 1934 by Neyman. The articles suggest the optimum sample sizes to be selected from each stratum for which sampling variance of the estimator is minimum for fixed total cost of the survey or the cost is minimum for a fixed precision of the estimator. If in a sample survey more than one characteristic is to be measured on each selected unit of the sample, that is, the survey is a multi-response survey, then the problem of determining the optimum sample sizes to various strata becomes more complex because of the non-availability of a single optimality criterion that suits all the characteristics. Many authors discussed compromise criterion that provides a compromise allocation, which is optimum for all characteristics, at least in some sense. Almost all of these authors worked out the compromise allocation by minimizing some function of the sampling variances of the estimators under a single cost constraint. A serious objection to this approach is that the variances are not unit free so that minimizing any function of variances may not be an appropriate objective to obtain a compromise allocation. This fact suggests the use of coefficient of variations instead of variances. In the present article, the problem of compromise allocation is formulated as a multi-objective non-linear programming problem. By linearizing the non-linear objective functions at their individual optima, the problem is approximated to an integer linear programming problem. Goal programming technique is then used to obtain a solution to the approximated problem.     

基于信息准则的最优组合预测小样本改进模型

在对样本量小且波动大的变量进行预测时,最优组合模型往往容易出现过拟合问题而导致预测效果不佳.借鉴信息准则中对过拟合问题的处理方式,结合等权组合在预测实践中的良好表现,通过在最优组合模型的目标方程中增加向等权收缩的惩罚项,建立了最优组合预测小样本改进的二次规划模型.最后通过实例,用最优组合预测和其他常用组合预测方法结果的比较,说明了该方法的可行性和有效性.     

A Stochastic Approach to General Nonlinear Programming Problems

Nonlinear programming problem is the general case of mathematical programming problem such that both the objective and constraint functions are nonlinear and is the most difficult case of smooth optimization problem to solve. In this article, we suggest a stochastic search method to general nonlinear programming problems which is not an iterative algorithm but it is an interior point method. The proposed method finds the near-optimal solution to the problem. The results of a few numerical studies are reported. The efficiency of the new method is compared and is found to be reasonable.