Multivariate L1 mean

The center of a univariate data set {x ₁,…,x _n} can be defined as the point μ that minimizes the norm of the vector of distances y′=(|x ₁−μ|,…,|x _n−μ|). As the median and the mean are the minimizers of respectively the L ₁- and the L ₂-norm of y, they are two alternatives to describe the center of a univariate data set. The center μ of a multivariate data set {x ₁,…,x _n} can also be defined as minimizer of the norm of a vector of distances. In multivariate situations however, there are several kinds of distances. In this note, we consider the vector of L ₁-distances y′₁=(∥x ₁- μ∥₁,…,∥x _n- μ∥₁) and the vector of L ₂-distances y′₂=(∥x ₁- μ∥₂,…,∥x _n-μ∥₂). We define the L ₁-median and the L ₁-mean as the minimizers of respectively the L ₁- and the L ₂-norm of y ₁; and then the L ₂-median and the L ₂-mean as the minimizers of respectively the L ₁- and the L ₂-norm of y ₂. In doing so, we obtain four alternatives to describe the center of a multivariate data set. While three of them have been already investigated in the statistical literature, the L ₁-mean appears to be a new concept. Received January 1999     

Time-consistent investment policies in Markovian markets: A case of mean–variance analysis

The optimal investment policy for a standard multi-period mean–variance model is not time-consistent because the variance operator is not separable in the sense of the dynamic programming principle. With a nested conditional expectation mapping, we develop an investment model with time consistency in Markovian markets. Furthermore, we examine the differences of the investment policies with a riskless asset from those without a riskless asset. Analytical solutions for time-consistent optimal investment policies and the resulting mean–variance efficient frontier are obtained. Finally, using numerical examples, we show that the optimal investment policy derived from our model is more efficient than that of the standard mean–variance model in which the trade-off is determined between the mean and variance of the terminal wealth.     

Large time and small noise asymptotic results for mean reverting diffusion processes with applications

Summary. We use the theory of large deviations to investigate the large time behavior and the small noise asymptotics of random economic processes whose evolutions are governed by mean-reverting stochastic differential equations with (i) constant and (ii) state dependent noise terms. We explicitly show that the probability is exponentially small that the time averages of these process will occupy regions distinct from their stable equilibrium position. We also demonstrate that as the noise parameter decreases, there is an exponential convergence to the stable position. Applications of large deviation techniques and public policy implications of our results for regulators are explored. Received: December 7, 1998; revised version: October 25, 1999     

Deciphering robust portfolios

Robust portfolio optimization has been developed to resolve the high sensitivity to inputs of the Markowitz mean–variance model. Although much effort has been put into forming robust portfolios, there have not been many attempts to analyze the characteristics of portfolios formed from robust optimization. We investigate the behavior of robust portfolios by analytically describing how robustness leads to higher dependency on factor movements. Focusing on the robust formulation with an ellipsoidal uncertainty set for expected returns, we show that as the robustness of a portfolio increases, its optimal weights approach the portfolio with variance that is maximally explained by factors.     

Keeping up with the Joneses and optimal diversification

Peer-effects have been shown to affect behavior, and can generally lead to investments choices that are mean–variance inefficient. This paper analyzes optimal diversification with peer-effects. We show that if individuals have keeping-up with the Joneses preferences and they take their peer-group reference as the market portfolio, Markowitz’s mean–variance efficiency analysis and the CAPM equilibrium are intact. This holds for any keeping-up preferences, as well as heterogeneous combinations of such preferences. These results also extend to the Merton–Levy segmented-market model.     

逆向物流的战略价值

随着我国企业参与国际竞争越加频繁,以及国内政府、公众对环保的重视,逆向物流领域的研究不断深入。本文首先阐明逆向物流的内涵和理解,以不同视角评价企业实施逆向物流的战略价值,并结合我国实际情况探讨了逆向物流的管理方法,为我国企业实施逆向物流战略提供借鉴。     

浅析我国逆向物流的发展现状及对策

回收物流与废弃物流在生产和消费环节都会不断产生,尽管它们不能直接给企业带来效益,但非常有发展潜力。文章通过对我国逆向物流的现状分析,指出重视再生资源回收利用的迫切性,以及现阶段有效减少废弃物排放,增加资源利用的途径。     

Iterative Density Estimation from Contaminated Observations

We introduce an iterative procedure for estimating the unknown density of a random variable X from n independent copies of Y=X+ɛ, where ɛ is normally distributed measurement error independent of X. Mean integrated squared error convergence rates are studied over function classes arising from Fourier conditions. Minimax rates are derived for these classes. It is found that the sequence of estimators defined by the iterative procedure attains the optimal rates. In addition, it is shown that the sequence of estimators converges exponentially fast to an estimator within the class of deconvoluting kernel density estimators. The iterative scheme shows how, in practice, density estimation from indirect observations may be performed by simply correcting an appropriate ordinary density estimator. This allows to assess the effect that the perturbation due to contamination by ɛ has on the density to be estimated. We also suggest a method to select the smoothing parameter required by the iterative approach and, utilizing this method, perform a simulation study.     

孔子中庸哲学的双重内涵

"中庸"作为中国儒家哲学的核心概念,由孔子提出。孔子不惟提出了这一个概念,还通过言传身教的方式对其内涵进行了初步的界定。在孔子看来,"中庸"首先是一种至高无上的道德标准,与古圣先王的道德和人格紧密相连的,同时又是一脉相传的治国经验,是指导人们立身行事的行为准则。"中庸"既具有道德哲学的内涵,又具有生活哲学的内涵。     

上海住宅价格的解释——基于自回归均值回复模型的分析

使用1998年1月至2013年7月间月度上海住宅价格指数，采用自回归均值回复模型（ARMR），尝试对上海住宅价格进行解释。模型效果测试表明模型与实际住宅价格指数之间匹配良好。上海房价均衡月度增长率为0．77％；自回归系数显示43％的前两个月增长率将持续到当月；均值回复系数表明如果上月房价高出（低于）均衡水平1个百分点，下月房价增长率将下降（增加）大约0．022个百分点。