马科维兹投资组合的改进及其应用

通过对马科维兹(Markowitz)投资组合模型的简要分析,指出其存在缺陷,并借助熵理论对其进行了改进,拓展了熵理论在连续变量(正态分布)上的应用。通过构造性实例研究表明,改进的模型具有理论意义,可以帮助投资者针对具体的实际情况作出风险投资组合的最优投资决策。     

ROBUST ESTIMATION UNDER TYPE II CENSORING

The properties of robust M-estimators with type II censored failure time data are considered. The optimal members within two classes of ψ-functions are characterized. The first optimality result is the censored data analogue of the optimality result described in Hampel et al. (1986); the estimators corresponding to the optimal members within this class are referred to as the optimal robust estimators. The second result pertains to a restricted class of ψ-functions which is the analogue of the class of ψ-functions considered in James (1986) for randomly censored data; the estimators corresponding to the optimal members within this restricted class are referred to as the optimal James-type estimators. We examine the usefulness of the two classes of ψ-functions and find that the breakdown point and efficiency of the optimal James-type estimators compare favourably with those of the corresponding optimal robust estimators. From the computational point of view, the optimal James-type ψ-functions are readily obtainable from the optimal ψ-functions in the uncensored case. The ψ-functions for the optimal robust estimators require a separate algorithm which is provided. A data set illustrates the optimal robust estimators for the parameters of the extreme value distribution.     

AN ALGORITHM FOR THE DESIGN OF 2? FACTORIAL EXPERIMENTS ON CONTINUOUS PROCESSES

Saunders & Eccleston (1992) presented an approach to the design of 2-level factorial experiments for continuous processes. It determined sets of contrasts between the observations that could be well estimated, and then selected a design so that those contrasts estimated the parameters of interest. This paper shows that a well-estimated contrast must have a large number of changes of sign or level, and also be ‘paired’ in a particular sense. It develops an algorithm which constructs designs that must have a large number of changes of sign, evenly spread among the contrasts and optimal or near optimal. When such designs exist they are often preferable to those produced by the reverse foldover algorithm of Cheng & Steinberg (1991).     

DETERMINATION OF DOMAINS OF ATTRACTION BASED ON A SEQUENCE OF MAXIMA

Suppose that the maximum of a random sample from a distribution F(x) may be obtained in each of k equally spaced observation periods. This paper proposes a test to determine the domain of attraction of F(x), and investigates the properties when the sample size is very large and perhaps unknown and k is fixed and small. The test statistic is a function of the spacings between the order statistics based on the sequence of maxima and is suggested by reference to one studied previously when inference was based on the largest k observations of a random sample. A Monte Carlo study shows that the proposed test is more powerful than its main competitor. The test is illustrated by two examples.     

Binary-image restoration

We consider the problem of binary-image restoration. The image being restored is not random, and we make no assumption about the nature of its contents. The estimate of the colour at each site is a fixed (the same for all sites) function of the data available in a neighbourhood of that site. Under this restriction, the estimate minimizing the overall mean squared error of prediction is the conditional expectation of the true colour given the observations in the neighbourhood of a site. The computation of this conditional expectation leads to the formal definition of the local characteristics of an image, namely, the frequency with which each pattern appears in the true unobserved image. When the “true” distribution of the patterns is unknown, it can be estimated from the records. The conditional expectation described above can then be evaluated using the estimated distribution of the patterns, and this procedure leads to a very natural estimate of the colour at each site. We propose two unbiased and consistent estimates for the distribution of patterns when the noise is a Gaussian white noise. Since the size of realistic images is very large, the estimated pattern distribution is usually close to the true one. This suggests that the estimated conditional expectation can be expected to be nearly optimal. An interesting feature of the proposed restoration methods is that they do not require prior knowledge of the local or global properties of the true underlying image. Several examples based on synthetic images show that the new methods perform fairly well for a variety of images with different degrees of colour continuity or textures.     

AN ALGORITHM FOR CHOOSING THE SAMPLING TIMES FOR AN EXPERIMENT ON A CONTINUOUS PROCESS

Saunders & Eccleston (1992) and Saunders, Eccleston & Spessa (1992) developed an approach to the design of factorial experiments on continuous processes that allows for the correlation present in such processes. Their methods concentrated on identifying the order of application of treatments in such experiments, assuming that the spacing between experiments is constant. On a continuous process, there is no necessity to maintain equally spaced sampling times. This paper gives an algorithm for choosing the optimal sampling times for a factorial experiment aimed at estimating a particular parameter or set of parameters. It is shown that in practical situations the optimal sampling times give considerable improvements in the accuracy of the parameter estimates.     

α—较多最优解的梯度特性

对于多目标规划的α—较多最优解,本文给出目标函数的梯度特性.     

Temptation and Taxation

We study optimal taxation when consumers have temptation and self‐control problems. Embedding the class of preferences developed by Gul and Pesendorfer into a standard macroeconomic setting, we first prove, in a two‐period model, that the optimal policy is to subsidize savings when consumers are tempted by “excessive” impatience. The savings subsidy improves welfare because it makes succumbing to temptation less attractive. We then study an economy with a long but finite horizon which nests, as a special case, the Phelps–Pollak–Laibson multiple‐selves model (thereby providing guidance on how to evaluate welfare in this model). We prove that when period utility is logarithmic, the optimal savings subsidies increase over time for any finite horizon. Moreover, as the horizon grows large, the optimal policy prescribes a constant subsidy, in contrast to the well known Chamley–Judd result.     

政府补偿下基于私人公平偏好的PPP项目投资决策分析

针对PPP （Private-Public Partnership）项目收益的不确定性,引入政府补偿契约问题。考虑私人投资者对政府补偿存在公平偏好倾向,借鉴BO模型的思想,将私人投资要求的特许收益作为其公平参考点,并通过对FS模型加以改进,构建私人公平偏好效用函数,从而给出私人在政府补偿下的投资决策模型。通过模型求最优解和概率分析,探讨私人公平偏好对其最优投资决策的影响,并借助数值分析给予检验。结果表明:当政府补偿使私人感知有利不公平时,私人将选择期望效用最大的最优投资,并随其感知程度的增加而增加;而当政府补偿使私人感知不利不公平时,私人最优投资及可能性将在有限公平偏好内随其感知程度的增加而减小。     

产业共性技术扩散中政府作用最优力度分析——基于变换的Bass模型

基于一定理论假设将Bass模型中技术扩散的内部影响因素和外部影响因素分别与市场作用和政府作用对应起来,并着眼于政府作用对市场作用的“挤出”效应建立起政府作用与市场作用之间的函数关系,以此来对Bass模型进行变换,使其能刻画政府作用对产业共性技术扩散速度和时间路径的影响。基于变换的Bass模型,以最大化技术扩散速度为目标构建最优化问题以求得政府作用最优力度,由最优化问题可知政府作用对市场作用的“挤出”效应越大,最优政府作用力度就应该越小。还基于相关数据进行了数值模拟分析,并且验证了模型的有效性。研究认为:由于存在政府干预对市场作用的“挤出”效应,在促进产业共性技术扩散中需要把握最优的干预力度即政府作用最优力度,在量化政府作用和市场作用的基础上,求解出来的政府作用最优力度系数可为政府有效和适当干预技术扩散提供理论上的一个尺量。