Time-consistent investment strategy under partial information

This paper considers a mean–variance portfolio selection problem under partial information, that is, the investor can observe the risky asset price with random drift which is not directly observable in financial markets. Since the dynamic mean–variance portfolio selection problem is time inconsistent, to seek the time-consistent investment strategy, the optimization problem is formulated and tackled in a game theoretic framework. Closed-form expressions of the equilibrium investment strategy and the corresponding equilibrium value function under partial information are derived by solving an extended Hamilton–Jacobi–Bellman system of equations. In addition, the results are also given under complete information, which are need for the partial information case. Furthermore, some numerical examples are presented to illustrate the derived equilibrium investment strategies and numerical sensitivity analysis is provided.     

Distributionally robust chance constrained problem under interval distribution information

This paper is concerned with distributionally robust chance constrained problem under interval distribution information. Using worst-case CVaR approximation, we present a tractable convex programming approximation for distributionally robust individual chance constrained problem under interval sets of mean and covariance information. We prove the worst-case CVaR approximation problem is an exact form of the distributionally robust individual chance constrained problem. Then, our result is applied to worst-case Value-at-Risk optimization problem. Moreover, we discuss the problem under several ambiguous distribution information and investigate tractable approximations for distributionally robust joint chance constrained problem. Finally, we provide an illustrative example to show our results.     

Minimaxity and nonminimaxity of a preliminary test estimator for the multivariate normal mean

Summary The problem is to estimate the mean of ap-dimensional normal distribution in the situation where there is vague information that the mean vector might be equal to zero vector. Minimax property of the preliminary test estimator obtained by the use of AIC (Akaike's Information Criterion) procedure is discussed under a loss function which is based on Kullback-Leibler information measure and evaluates both an error of model selection and that of estimation. Whenp is even, the minimaxity is shown to hold for small values ofp but not for large values.     

A predictive estimator of finite population mean using nonparametric regression

The paper considers the problem of estimating the population mean using auxiliary information. We propose a new model-based estimator of the population mean, based on local polynomial regression. This estimator exhibits several attractive properties under the model-based approach. The estimator is compared to a number of methods which have been proposed in the literature via a simulation study based on several populations.     

Uncertain linguistic Bonferroni mean operators and their application to multiple attribute decision making

In this paper, we investigate the multiple attribute decision making (MADM) problems with uncertain linguistic information. Motivated by the ideal of Bonferroni mean and geometric Bonferroni mean, we develop two aggregation techniques called the uncertain linguistic Bonferroni mean (ULBM) operator and the uncertain linguistic geometric Bonferroni mean (ULGBM) operator for aggregating the uncertain linguistic information. We study its properties and discuss its special cases. For the situations where the input arguments have different importance, we then define the uncertain linguistic weighted Bonferroni mean (ULWBM) operator and the uncertain linguistic weighted geometric Bonferroni mean (ULWGBM) operator, based on which we develop two procedures for multiple attribute decision making under the uncertain linguistic environments. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.     

A new multiple attribute group decision making method in intuitionistic fuzzy setting

The multiple attribute group decision making (MAGDM) problem with intuitionistic fuzzy information investigated in this paper is very useful for solving complicated decision problems under uncertain circumstances. Since experts have their own characteristics, they are familiar with some of the attributes, but not others, the weights of the decision makers to different attributes should be different. We derive the weights of the decision makers by aggregating the individual intuitionistic fuzzy decision matrices into a collective intuitionistic fuzzy decision matrix. The expert has a big weight if his evaluation value is close to the mean value and has a small weight if his evaluation value is far from the mean value. For the incomplete attribute weight information, we establish some optimization models to determine the attribute weights. Furthermore, we develop several algorithms for ranking alternatives under different situations, and then extend the developed models and algorithms to the MAGDM problem with interval-valued intuitionistic fuzzy information. Numerical results finally illustrate the practicality and efficiency of our new algorithms.     

广义自回归模型参数的收缩估计

运用经典方法结合参数的先验信息得到了广义一阶自回归模型中自相关系数的收缩估计的闭式表达式,它是通常极大似然估计与先验均值的加权平均,在适当的先验信息下优于原来的估计.     

Quick response policy with Bayesian information updates

In this paper we investigate the quick response (QR) policy with different Bayesian models. Under QR policy, a retailer can collect market information from the sales of a pre-seasonal product whose demand is closely related to a seasonal product’s demand. This information is then used to update the distribution for the seasonal product’s demand by a Bayesian approach. We study two information update models: one with the revision of an unknown mean, and the other with the revision of both an unknown mean and an unknown variance. The impacts of the information updates under both models are compared and discussed. We also identify the features of the pre-seasonal product which can bring more significant profit improvement. We conclude that an effective QR policy depends on a precise information update model as well as a selection of an appropriate pre-seasonal product as the observation target.     

基于回购契约的供应链鲁棒协调模型

研究了需求不确定条件下供应链回购契约协调问题。针对未知需求具体分布形式的两级供应链系统,建立了基于回购契约的供应链鲁棒协调模型。给出了仅知需求均值和方差信息条件下,集成供应链系统的鲁棒订货策略和分散供应链系统的鲁棒契约协调策略。分析了不同契约参数条件下的供应链及其成员利润情况。最后,进行了数值计算,验证了当获得需求的真实分布形式时．供应链鲁棒回购契约协调策略的有效性。结果表明,供应链鲁棒回购契约协调策略能够有效减少需求不确定性对系统及其成员利润的影响。     

Bayes估计的进一步研究及其Pitman最优性

对线性模型参数,讨论了Bayes估计的Pitman最优性,将已有结果进行了改进,去掉了附加条件,证明了在Pitman准则下,Bayes估计一致优于最小二乘估计(LSE),在此基础上,提出了一种基于先验信息的方差分量估计,通过和基于LSE的方差分量估计作比较,证明了新估计是无偏估计且有更小的均方误差．最后,证明了在Pitman准则下生长曲线模型参数的Bayes估计优于最佳线性无偏估计．     

roperties and Applications of Alpha Power Gamma Distribution

In this paper, the gamma distribution has been extended by adding an extra shape parameter, we refer to the new distribution as alpha power gamma distribution. It is found that the distribution has a relatively flexible hazard rate function. The properties of the new distribution are studied, including explicit expressions for the $s^{\text{th}}$ raw moments, moment generating function and distributions of order statistics are derived. Also, the integral expressions for the entropy, mean residual life and mean waiting time are obtained. The maximum likelihood estimators of the distribution parameters under complete sample are discussed, the Fisher information matrix is derived. Then, the estimation of the parameters under the general progressive type-II censoring is studied. Finally, the real data set is used to illustrate the practicality of the proposed distribution.     

利用分层抽样数据中完全辅助信息的模型校正方法

In stratified survey sampling, sometimes we have complete auxiliary information. One of the fundamental questions is how to effectively use the complete auxiliary information at the estimation stage. In this paper, we extend the model-calibration method to obtain estimators of the finite population mean by using complete auxiliary information from stratified sampling survey data. We show that the resulting estimators effectively use auxiliary information at the estimation stage and possess a number of attractive features such as asymptotically design-unbiased irrespective of the working model and approximately model-unbiased under the model. When a linear working-model is used, the resulting estimators reduce to the usual calibration estimator(or GREG).     

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??In this paper, the gamma distribution has been extended by adding an extra shape parameter, we refer to the new distribution as alpha power gamma distribution. It is found that the distribution has a relatively flexible hazard rate function. The properties of the new distribution are studied, including explicit expressions for the $s^{\text{th}}$ raw moments, moment generating function and distributions of order statistics are derived. Also, the integral expressions for the entropy, mean residual life and mean waiting time are obtained. The maximum likelihood estimators of the distribution parameters under complete sample are discussed, the Fisher information matrix is derived. Then, the estimation of the parameters under the general progressive type-II censoring is studied. Finally, the real data set is used to illustrate the practicality of the proposed distribution.     

双辅助信息敏感性问题问卷调查技术

对于敏感性问题调查,已有多种随机化策略.提出一类方便、实用的双辅助信息间接问卷调查方法,讨论了估计量及其方差以及精度与保护度之间的关系.通过比较得出,在相同的保护度下,随机化方法与问卷方法在精度上各有得益.     

有辅助信息时有限总体分布函数的新估计量

本文提出两个新的估计量,利用观察数据中的总体辅助信息来估计有限总体分布函数,并通过两个人工总体的模拟实验,比较新的估计量、传统的估计量及Rao,Kover&Mantel(1990)提出的估计量的相对平均误差与相对标准差。结果表明,从相对标准差的角度分析,两个新的估计量有一个是四个估计量中精度最好的一个,另一个也有很好的表现;而且它们在模型有所偏差时都具备了较好的稳健性。     

The averaging method and the persistence of attractors

The theorems that are presented in this paper, are a contribution to the foundations of the averaging method for ordinary differential equations. They involve the study of the persistent features of vector fields, under non autonomous perturbations of mean value zero. The problem of obtain ing qualitative information from the study of the averaged equation is considered and theorems that give new conditions to guarantee the uniform validitv of the approximation over the time interval [ 0.∞), are proved. A general icsult on the persistence of attractors is presented. The analysis uses in a fundamental way, a generalization of the notion of a solution stable under persistent disturbances. The proofs do not require special behavior of the linearized system and the results obtained are not only local, but give relevant information about the persistence of domains of attraction.     

Empirical Likelihood Inference Under Stratified Random Sampling in the Presence of Measurement Error

Suppose that several different imperfect instruments and one perfect instrument are used independently to measure some characteristic of a population. In order to make full use of the sample information, in this paper the empirical likelihood method is put forward for making inferences on parameters of interest under stratified random sampling in the presence of measurement error, Our results show that it can lead to estimators which are asymptotically normal and utilize all the available sample information. We also obtain the asymptotic distribution of empirical likelihood testing statistics. In particular, we apply the method to obtain estimator and confidence interval of population mean.     

基于先验信息的社会碳成本贝叶斯不确定性分析

针对气候变化及经济影响存在的巨大不确定性,研究了气候变化不确定性以及先验信息对社会碳成本的影响.在贝叶斯理论框架下,采用指数分布刻画气候变化的分布特征,假设尾部变化率是一个随机变量,给出其伽玛先验分布,推导了气候变化分布的贝叶斯先验预测分布.并分别基于指数分布以及帕累托先验预测分布计算了社会碳排放成本.模拟分析发现,在未融合先验信息的情况下,由于尾部概率很小,不管是否修正消费与气候变化之间的关系,截尾社会碳成本和未截尾社会碳成本几乎重合.然而,在利用贝叶斯方法融合先验信息的情况下,社会碳成本容易受到先验信息的影响.但是,通过修正消费与气候变化之间的关系后,发现社会碳成本受先验信息的影响比较少.     

On the informative power of all possible linear functionals for the discretization of solutions of the Klein-Gordon equation in the metric of <Emphasis Type="Italic">L</Emphasis><Superscript>2,∞</Superscript>

For the Klein-Gordon equation with initial conditions in Nikol’skii classes, we obtain sharp orders of discretization errors with respect to precise information. In particular, these orders imply qualitatively and quantitatively that raising the smoothness of one of the initial conditions relative to the other does not improve the discretization characteristics of the solution of the equation. Bounds for information distortion are given under which the limit possible errors, i.e., discretization errors with respect to precise information, are still maintained. This is important because superfluous computational accuracy used when implementing an algorithm results in an unjustified increase in memory requirements and the number of arithmetic operations without improving the accuracy inherent to the algorithm. The quality of approximation aggregates is also estimated in mean square with respect to probability measures on Nikol’skii classes.     

企业间信息共享的激励问题研究

本文考虑了一个零售商占主导地位但制造商具有市场需求信息优势的二级供应链系统;具体来说,制造商具有确定的市场需求信息,而零售商对市场需求信息仅仅有一个随机先验分布。本文讨论的问题是,当零售商设计采购合同时,制造商是否有意愿去改善零售商的需求信息？如果可能,是否零售商提供的合同越复杂越能激励制造商这么做呢？本文的研究结果表明,(i)制造商希望零售商需求估计的均值(即信息趋势)尽可能地低。但是对于需求估计的方差(即信息精度),则存在一个临界值,低于这个值时,制造商希望零售商需求的方差越大越好;高于这个值时,制造商希望零售商需求的方差越小越好,这意味着制造商在某种程度上愿意与零售商共享信息;(ii)复杂的合同并不能提供更多的激励去促使制造商共享信息。本文的结论意味着需要设计新的机制去促使制造商能够诚实地披露他的私有信息。