导数在研究初等函数上的应用

在当今数学分析的诸多方面，导数是研究函数性质的一个强有力工具。首先从导数的的概念及其几何意义入手，其次研究函数的单调性、极值、最值、凸凹性、拐点及函数作图等。最后选取一些典型的问题，用导数进行刻画。     

多元函数极值的应用研究

函数极值不仅是函数性态的一个重要特征,而且在实际问题中占有重要的地位。尤其是在当今日益发展的社会生活中,工农业生产、自然科学和工程技术等发展带来了大量的问题,其实质都是函数极值问题。多元函数极值则通过现在经济学中的热点问题——利润最大化和消费者效用最大化来体现。     

独立学院数学改革之数学实验——Matlab平台上“四步法”研究函数的单调性与凹凸性

数学实验是高等数学改革的重要方向,借助数学软件简化数学计算,注重数学应用是数学教学的一个新动向。函数的单调性与凹凸性是高等数学中导数应用部分的一个重要内容。本文借助功能强大的数学软件Matlab,巧用计算与图形功能,提出应用导数研究函数的单调性与凹凸性的四步法,即(1)求导函数;(2)求导函数的零点;(3)画原函数与导函数图;(4)确定函数的单调性或凹凸性。该方法采用先求导函数零点再画图的顺序,确保画图区域包含导函数的零点,避免遗漏极值点或拐点,进一步通过实例系统体现该方法对函数单调性与凹凸性的可视化判定。     

函数的极值与MATLAB应用

函数的极值是高等数学的重点和难点,本文讨论了如何借助多媒,运用MATLAB数学软件求函数的极值。     

多层标准厂房楼盖次梁间距优化设计

本文运用一维函数求极值法推导出了板的最优厚度、次梁最优高度，并用穷举法求出了在各种面荷载情况下所对应的最优次梁间距。实例计算表明，对次梁间距优化可使楼盖节省１０％左右。     

用几何画板软件探讨二元函数的条件极值问题

利用几何画板软件先绘制出约束条件的图象,再把图象上的动点代入二元函数,观测函数性态,寻求极值。     

基于二分法的函数图像描绘

本文结合导数研究函数的单调性、凹凸性的方法,从二分法的基本思想入手,用二分法描绘函数图像,得出二分法求拐点横坐标近似值、描绘函数的图像的基本步骤,进而拓展了二分法的应用。     

极值统计理论在金融风险中的应用

本文考察外汇交易中由于汇率的急剧变化可能引起的巨大损失,应用极值统计方法估计风险价值,并与经验分布函数进行比较,得到了很好的结果,通过对29年来的日元／美元汇率的实证分析,说明极值方法在统计风险价值中的应用。     

独立学院高等数学教学中融入数学实验的实践

本文分析了在独立学院高等数学中融入数学实验的意义,并通过教学实例二元函数极值,说明了具体的教学设计过程。     

基于带极值扰动粒子群算法的不确定性需求下最优采购决策

通过分析采用模糊数学方法拟合具有明显时间和季节变化规律的不确定需求比一般随机分布函数具有显著优势的原因,建立了基于模糊数学的最优采购决策模型。基于数理推导和证明,设计了带极值扰动的优化粒子群算法。通过实验证明了改进的优化算法在收敛速度、精度以及摆脱局部极值的能力上有大幅提高,是一种实用而高效的优化算法。     

Statistics of extreme events in risk management: The impact of the subprime and global financial crisis on the German stock market

Given the growing need for managing financial risk and the recent global crisis, risk prediction is a crucial issue in banking and finance. In this paper, we show how recent advances in the statistical analysis of extreme events can provide solid methodological fundamentals for modeling extreme events. Our approach uses self-exciting marked point processes for estimating the tail of loss distributions. The main result is that the time between extreme events plays an important role in the statistical analysis of these events and could therefore be useful to forecast the size and intensity of future extreme events in financial markets. We illustrate this point by measuring the impact of the subprime and global financial crisis on the German stock market in extenso, and briefly as a benchmark in the US stock market. With the help of our fitted models, we backtest the Value at Risk at various quantiles to assess the likeliness of different extreme movements on the DAX, S&P 500 and Nasdaq stock market indices during the crisis. The results show that the proposed models provide accurate risk measures according to the Basel Committee and make better use of the available information.     

上市公司高管-员工薪酬差距与经营业绩关系实证研究

用2005-2012年我国上市公司的面板数据,研究了高管-员工薪酬差距与公司经营业绩之间的关系,发现高管-员工薪酬差距对公司经营业绩的影响呈现倒U型结构,并存在一个最有利于公司经营业绩成长的极值点。在到达极值点之前,高管-员工薪酬差距对公司经营业绩的影响表现为正效应,在达到极值点之后表现为负效应。实证结果也发现,地区、产权、资金周转率、员工人数、员工受教育程度等因素均会影响公司经营业绩,并且发达地区和非国有上市公司的极值点较大,可以承受更大的高管-员工薪酬差距。     

基于极值理论和Bootstrap方法的E-VaR研究和实证分析

考虑金融时间序列的厚尾特性,讨论了应用极值理论中的广义Pareto分布模型度量风险的问题。利用Bootstrap和MLE方法对参数进行点估计和区间估计,得出E-VaR的估计值,并对深证综指收益进行实证分析,探讨与尾部相关的极值风险,结果令人满意。     

Mutual excitation between OECD stock and oil markets: A conditional intensity extreme value approach

We analyze the degree of mutual excitation that exists between extreme events across the stock markets of OECD member nations and the Brent and WTI crude oil markets. For this analysis, marked point process models are proposed which are able to capture the dynamics of the intensity of occurrence and comovement during periods of crisis. The results show a significant, negative interdependence between most OECD markets, especially those of the USA, Japan and France. These major oil importing countries display links between equity market losses and positive returns in both oil markets. However, positive interdependence is not observed between any of the OECD countries except for South Korea. The great advantage of this methodology is that, apart from using the size distribution of extreme events, it also uses the occurrence times of extreme events as a source of information. With this information, these models are better able to capture the stylized facts of extreme events in financial markets such as clustering behavior and cross-excitation.     

Extreme returns and intensity of trading

Asymmetric information models of market microstructure claim that variables such as trading intensity are proxies for latent information on the value of financial assets. We consider the interval‐valued time series (ITS) of low/high returns and explore the relationship between these extreme returns and the intensity of trading. We assume that the returns (or prices) are generated by a latent process with some unknown conditional density. At each period of time, from this density, we have some random draws (trades) and the lowest and highest returns are the realized extreme observations of the latent process over the sample of draws. In this context, we propose a semiparametric model of extreme returns that exploits the results provided by extreme value theory. If properly centered and standardized extremes have well‐defined limiting distributions, the conditional mean of extreme returns is a nonlinear function of the conditional moments of the latent process and of the conditional intensity of the process that governs the number of draws. We implement a two‐step estimation procedure. First, we estimate parametrically the regressors that will enter into the nonlinear function, and in a second step we estimate nonparametrically the conditional mean of extreme returns as a function of the generated regressors. Unlike current models for ITS, the proposed semiparametric model is robust to misspecification of the conditional density of the latent process. We fit several nonlinear and linear models to the 5‐minute and 1‐minute low/high returns to seven major banks and technology stocks, and find that the nonlinear specification is superior to the current linear models and that the conditional volatility of the latent process and the conditional intensity of the trading process are major drivers of the dynamics of extreme returns.     

Extreme value statistics for censored data with heavy tails under competing risks

This paper addresses the problem of estimating, from randomly censored data subject to competing risks, the extreme value index of the (sub)-distribution function associated to one particular cause, in a heavy-tail framework. Asymptotic normality of the proposed estimator is established. This estimator has the form of an Aalen-Johansen integral and is the first estimator proposed in this context. Estimation of extreme quantiles of the cumulative incidence function is then addressed as a consequence. A small simulation study exhibits the performances for finite samples.     

Abnormal returns, risk, and options in large data sets

Large data sets in finance with millions of observations have become widely available. Such data sets enable the construction of reliable semi-parametric estimates of the risk associated with extreme price movements. Our approach is based on semi-parametric statistical extreme value analysis, and compares favorably with the conventional finance normal distribution based approach. It is shown that the efficiency of the estimator of the extreme returns may benefit from high frequency data. Empirical tail shapes are calculated for the German Mark—US Dollar foreign exchange rate, and we use the semi-parametric tail estimates in combination with the empirical distribution function to evaluate the returns on exotic options.     

Joint behavior of point process of exceedances and partial sum from a Gaussian sequence

Consider a triangular array of mean zero Gaussian random variables. Under some weak conditions this paper proves that the partial sums and the point processes of exceedances formed by the array are asymptotically independent. For a standardized stationary Gaussian sequence, it is shown under some mild conditions that the point process of exceedances formed by the sequence (after centered at the sample mean) converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. Finally, the joint limiting distributions of the extreme order statistics and the partial sums are obtained.     

The self-employed without employees—autonomous or atypical?

The 1980s and early 1990s have witnessed a substantial growth in the self-employed component of the national labour-force. Of these, around two-thirds are one-person businesses without employees. This article identifies an occupational grouping which occupies a position at the extreme point on a continuum of small business independence, virtually indistinguishable from that of employees.     

高铁综合交通枢纽对周边区域影响研究——以北京南站为例

高铁综合交通枢纽具有交通功能和城市功能两个基本属性,对周边区域产生节点效应和场所效应。这两种效应的发展关系存在着六种不同发展类型,即:过多节点效应发展、相互依赖发展、相互紧张发展、平衡发展、相互调整发展和过多场所效应发展。文章以北京南站为例,发现北京南站目前属于过多节点效应发展类型,北京南站过多的交通功能减弱了其对周边区域的城市功能,压制了其场所效应的发展。在北京南站后期发展过程中,需要政府根据实际特点进行相关产业发展的支持协调,寻求其节点效应和场所效应的最优平衡点,以发挥高铁枢纽站对周边区域发展影响的最大效应。