Fighting the arch–enemy with mathematics'

This is an account of theoretical and applied statistical work done in connection with the problem how to determine a safe height for the sea dikes in the Netherlands     

中国大陆与其主要贸易伙伴股市间的极值关联性

本文运用尾部相依系数作为度量极值关联性的工具,首先研究中国加入世界贸易组织后大陆股市与七个主要贸易伙伴股市的极值关联性强弱,即股市同时极端下跌的风险性大小;其次研究中国加入世界贸易组织前后大陆股市与世界股市整体的极值关联性变化情况。结果发现：相比欧美股市,中国大陆股市与亚洲股市联系更紧密,同时发生极端下跌的可能性更大。整体而言,中国大陆股市与世界其他股市配置资产已无法完全分散极值风险。因此,若投资者在中国大陆股市进行投资的同时也寻求其他国家或地区股市,为了降低极值风险发生的概率,应选择欧美国家的股市。     

利用GARCH-M类模型和极值理论对上证综指的研究

金融时间序列具有分布的厚尾性、波动的集聚性等特征,传统的方法难以准确的度量其风险。文中运用一种新的估计VaR和ES的方法,即采取两阶段法。首先用GARCH-M类模型(GARCH-M、EGARCH-M和TGARCH-M)拟和原始收益率数据,得到残差序列;第二步用极值分析的方法分析的尾部,最后得到收益率序列的动态VaR和ES。最后对三个模型的计算结果进行比较。     

多元化经营对公司绩效的影响研究

本文假设企业规模在多元化经营与企业绩效的影响关系中具有中介作用,提出"多元化程度—公司规模—公司绩效"的变量模型;利用中国制造业上市公司2008～2010年的数据,通过横截面分析和面板数据分析对该模型进行实证检验。横截面分析结果表明,多元化经营对公司会计绩效产生负向影响,并且公司规模在其中具有部分中介作用,但对公司市场价值并不产生显著影响;面板数据分析结果显示,多元化经营对公司会计绩效和市场价值的影响都不显著。     

基于极值理论的资产组合风险研究

在金融系统中风险管理者十分关注投资风险的大小,尤其是在极端情况下的风险大小。市场风险值()是一种常用的度量风险的方法。本文将极值理论用于中国上证指数和深成指数市场风险值的度量,同时探讨了用极值理论评价资产组合风险的方法,并将其计算结果与基于正态分布同t分布的方法进行比较,发现采用极值理论度量市场风险值要优于经典的方法。     

An Extreme Value Approach to Test the Effect of Price Limits on Volatility

Many stock exchanges around the world enforcing daily price limits on the amount asset prices can change to prevent the market from overreacting and to reduce volatility. Price limits are artificial boundaries set by market regulators who restrict price changes of a stock to a pre-specified range during a trading day or a single trading session. The primary aim of price limit rules is to stabilize the markets during panic trading, to moderate vitality by repressing excessive speculation, and to allow stocks to be traded at prices close to their fair value. However, their impact on the market is a somewhat unresolved issue （Harris, 1998）. Using a methodology of comparing volatility based on the extreme value technique, the authors empirically investigate the impact of price limits on the volatility of the Stock Exchange of Thailand. The empirical results support price limits advocates, suggesting that price limits rules moderate stock price volatility.     

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.     

多元化战略程度与企业绩效实证研究

目前我国企业,尤其是中小企业的多元化经营过程中,跨行业成长并没有给其带来绩效的提高。本文结合我国中小板上市公司的数据及现状,提出了多元化战略程度与绩效相关的两个假设。其次,为了验证该假设,本文对假设中的概念进行操作性变量的定义,最后提出具体的模型并进行实证分析。     

Sociological Models Based on Fréchet Random Variables

Products of random variables are of both practical and theoretical significance to social scientists. This has increased the need to have available the widest possible range of statistical results on products of random variables. In this note, the distribution of the product XY is derived when X and Y are independent Fréchet random variables. Extensive tabulations of the associated percentage points are also given.     

The ascending ladder height distribution for a certain class of dependent random walks

A random walk { S_n } with S_n = (X_l - Y_l) +…+ ( X_n - Y_n ) is considered where the X_n Y_n are non-negative random variables, the Y_n are exponentially distributed with rate δ and the X_n have common distribution function B . It is shown that the expression δ(1 - S (x)) for the density of the ascending ladder height distribution of (S_n), which is well-known for i.i.d. X_n , holds also when the X_n form a stationary sequence of not necessarily independent random variables.     

Stability and self-decomposability of semi-group valued random variables

A random variable X on IR₊ is said to be self-decomposable, dif for all c∈ (0, 1) there exists a random variable X_c on IR₊ such that X=^dcX+X_c . It is said to be stable if it is self-decomposable and X_c=^d (1 - c)X' , where X and X' are identically and independently distributed. The notions of stability and self-decomposability for infinitely divisible random variables are generalised to abelian semi-groups ( S, + ) with S having an identical involution, by using characteristic functions. The generalised definitions involve semi-groups of scaling operators T . There operators can be interpreted in a slightly different context as generalised continuous-time branching processes (with immigration). The underlying importance of the generator of the semi-groups T in the characterisation of stability and self-decomposability is stressed.     

基于价值工程方法改进的多维Logit模型研究

通过引入价值工程方法,改进基于随机效用理论的多维Logit模型,形成VEL模型,对VEL模型进行了功能分析和广义出行成本分析,最后论述出行人群的划分方式和集计化。     

极端波动情景中的压力测试和极值理论方法研究

VaR描述的是市场正常波动情况下的资产组合最大可能损失,指出了不利事件发生的概率,但没有说明不利事件发生时的实际损失到底有多大。为了测量在这些小概率极端情况下的风险,本文对当前测量极端波动情景中较为先进的情景分析、系统化压力测试和极值分析方法进行较为全面的研究。     

On the Ratio of Fréchet Random Variables

The distribution of the ratio X/Y is derived when X and Y are independent Fréchet random variables. Extensive tabulations of the associated percentage points are also given.