Alternate approach to unify CAPM and APT

We utilize the joint elliptical distribution to model a multi-factor return generating process and derive an equilibrium multi-beta capital asset pricing model (CAPM) in which the market portfolio and a set of nonelliptical factors are sufficient to price all financial assets. Most important, it is shown that the market portfolio, while generally nonelliptical, can proxy all elliptical factors and hence: including elliptical factors in addition to the market portfolio in the pricing equation contribute nothing to asset pricing. While the representative investor prices the exposure of aggregate wealth to various nonelliptical systematic risk factors, individual securities are priced in accordance to their contributions to different aspects of the risk of aggregate wealth. The present model collapses to the Sharpe-Lintner CAPM when either the market investor is neutral to nonelliptical risk factors or when all risk factors follow a joint spherical distribution. When residuals cancel out of the market portfolio, the present model collapses to Conner (1984) pricing model.     

A characterization of the distributions that imply existence of linear equilibria in the Kyle-model

The existence of a linear equilibrium in Kyle’s model of market making with multiple, symmetrically informed strategic traders is implied for any number of strategic traders if the joint distribution of the underlying exogenous random variables is elliptical. The reverse implication has been shown for the case in which the random variables are independent and have finite second moments. Here we extend this result to the case in which the underlying random variables are not necessarily independent and their joint distribution is determined by its moments. We thank two anonymous referees for their comments. Financial support by the Deutsche Forschungsgemeinschaft, SFB-TR 15, is gratefully acknowledged.     

Increasing failure rate and decreasing reversed hazard rate properties of the minimum and maximum of multivariate distributions with log-concave densities

For a multivariate random vector X = (X ₁,...,X _n ) with a log-concave density function, it is shown that the minimum min{X ₁,...,X _n } has an increasing failure rate, and the maximum max{X ₁,...,X _n } has a decreasing reversed hazard rate. As an immediate consequence, the result of Gupta and Gupta (in Metrika 53:39–49, 2001) on the multivariate normal distribution is obtained. One error in Gupta and Gupta method is also pointed out.      

Applying public participation GIS (PPGIS) to inform and manage visitor conflict along multi-use trails

Managing visitor conflict is an important task in protected areas. This study used public participation GIS (PPGIS) mapping and a visitor survey to research conflicts between mountain bikers and horse riders, and other groups frequenting trails for tourism and recreation in national parks in northern Sydney (Australia). The goal was to evaluate the effectiveness of the PPGIS for determining conflict locations, and to integrate stated reasons and conflict resolution measures in a model. The survey showed that 42% of mountain bikers and 69% of horse riders had experienced conflicts, with each other, motorbike riders, walkers/hikers and dog walkers. PPGIS effectively mapped concurrent usage intensity to predict potential conflict locations over a reasonably large study area thereby identifying trails of the greatest concern. PPGIS also offered high-quality GIS visualisation options, and the novelty of the PPGIS increased participant engagement. We evaluated PPGIS compared to questionnaire-based surveying, direct visitor observations, GPS tracking, traffic counters and cameras. Because visitor conflict occurs within a spatial context, conflict management will require greater spatial knowledge of visitor activity, which can be obtained through the innovative PPGIS mapping. A conflict model is presented that integrates this study's empirical findings on conflict reasons and resolutions with existing conflict theory.     

A method to obtain new copulas from a given one

Given a strictly increasing continuous function φ from [0, 1] to [0, 1] and its pseudo-inverse φ^[−1], conditions that φ must satisfy for C_φ(x₁, . . . ,x_n)=φ^[−1](C(φ(x₁), . . . ,φ(x_n))) to be a copula for any copula C are studied. Some basic properties of the copulas obtained in this way are analyzed and several examples of generator functions φ that can be used to construct copulas C_φ are presented. In this manner, a method to obtain from a given copula C a variety of new copulas is provided. This method generalizes that used to construct Archimedean copulas in which the original copula C is the product copula, and it is related with mixtures     

Pareto Density Distributions

Building on new insights into the genesis ofPareto-Distributions,(“Kopp” effect etc.) as publishedearlier in “Quality and Quantity”, the author gives at least oneauthentic/definitive Pareto-Formula. A practical example of the synthetic generation of Pareto Distributions by means of spreadsheets. A working D.I.Y-method for fine-fitting Pareto-curvesto scattergrams with spreadsheets using interalia an indirect method of the least squares of residuals is fully demonstrated. A comparative test-fit to a cumulative Pareto- Distribution example, where a simulative curve-formula evolved by Prof. B. Arnold/Ucla is used for demonstration. Easy to absorb and to retain graphical tableaux are employed to visualize the chain of descent and interconnections between normal distributions, log-normal distributions and Pareto- Distributions. A quasi-dichotomy of the Pareto-formulae is presented in tableau-form. One innovative formula for Pareto-distribution is given as: F(x)= k^*e― [((ln(Integral(In(x)))) ‐ (ln(Integral(ln(μ)))))² / 2^*(ln(Integral(ln(σ))))²} Readers e-mailed constructive opinions &/or inputs are encouraged and welcomed. This revised version was published online in June 2006 with corrections to the Cover Date.     

光电效应测定普朗克常数中测量方法的讨论

分析了光电效应实验中实际测量普朗克常数时误差产生的原因，确定截止电压时应用交点法和拐点法相比较，并应用最小二乘法进行直线拟合求出较精确的普朗克常数值。     

旋转扶梯石材贴片的加工基准曲线拟合的数学模型

本文给出了旋转扶梯石材贴片的加工基准曲线拟合的数学模型，以空间螺旋线作为拟合曲线，为石材数控线切割机提供了理论基础，解决了石材加工行业中的实际问题，经实际检测应用，得到了令人满意的结果。     

秦皇岛市海岸线侵淤变化规律研究

海岸蚀退和港口淤积是当今世界各国港口城市迫切关注和急待解决的问题；秦皇岛市是我国环渤海经济区的重要港口城市。本文应用遥感手段，首次创新性地借助地理信息系统（ＧＩＳ）的支持，利用计算机图形图像处理与拟合技术对秦皇岛海岸侵淤时空演变进行定量评价；在此基础上，对其变化规律与影响因素进行了分析研究。最后认为：秦皇岛市现代海岸线总体呈蚀退形式；陆源物质入海量减少、海动力作用及沿岸工程建筑等是其海岸蚀退的主要影响因素。     

烟气湿法脱硫对烟囱的影响分析及防腐措施

烟气脱硫是火电厂对SO2排放进行控制的有效手段。针对湿法脱硫后产生的烟囱腐蚀问题,以鹿泉曲寨热电厂的脱硫改造工程为具体案例,分析了脱硫后烟囱内部烟气含水量高、腐蚀性强、温度低等特性,结合理论计算分析整个烟囱内的静压分布情况,并以此绘制静压分布曲线图,证明了由于烟气温度下降导致烟囱内部将出现正压区,从而导致内部烟气对烟囱的腐蚀加重,对4种烟囱防腐方案进行了综合比较,根据烟气运行工况、电厂使用年限以及烟囱结构型式等选择了切实可行的防腐方案。