基于Copula函数的华南台风极端灾害的重现期研究

利用1981-2014年华南地区的台风灾害数据,通过计算致灾因子的重现期来预测台风极端灾害频率,评估台风极端灾害的受灾程度.选取最大风速极值(X)和中心气压极值(Y)为研究变量,经过K-S检验选取最优的对数正态分布、正态分布分别作为X、Y的边缘分布,再通过Frank Copula函数构造联合分布,计算单变量重现期、联合重现期及同现重现期,并求出变量X与Y的设计值.计算结果发现,重现期不超过两年时,联合重现期的设计值要优于单变量重现期和同现重现期的设计值"重现期超过两年时,同现重现期的设计值要优于单变量重现期和联合重现期的设计值.最后以2015年至2017年台风中的X与Y作为输入,其重现期作为输出进行检验,结果与设计的组合重现期对比最优.研究结果表明,重现期小于等于两年时,选取联合重现期的设计值作为防灾标准"重现期大于两年时,选取同现重现期的设计值作为防灾标准,且致灾因子的重现期越长,台风极端灾害就越严重.     

基于组合权重和模糊随机方法的台风灾害风险评估

利用2000~2016年登陆华南地区的24个台风样本的灾情与致灾源数据,建立台风灾害风险评估模型。首先,运用层次分析法和熵权法构建一种新的组合权重;然后,利用组合权重构建灾情指数序列和致灾源指数序列,计算每个台风灾害风险值,并将风险值从小到大划分为五个区间;最后,采用模糊随机方法建立华南地区台风灾害模糊风险评估模型,计算得到五个风险等级区间的模糊可能性,以此来表示各等级台风灾害发生的可能性大小。结果表明,基于组合权重构造的灾情指数序列与致灾源指数序列相关性较强;华南地区发生第二风险等级台风灾害的可能性最大,发生第五风险等级台风灾害的可能性最小,与实际情况较为吻合。     

基于Copula-EVT模型的干旱灾害风险评估

干旱历时和干旱强度是影响干旱灾害风险的主要因素。根据干旱灾害发生的极端过程特点,用极值理论刻画干旱灾害风险两个特征变量的边缘分布,用Archimedes Copula函数捕捉旱灾风险两个特征变量之间的极值相依结构,本文构建的基于Copula-EVT的旱灾风险评估模型较好地反映了旱灾形成的极端过程和影响因子。实证分析以淮河流域蚌埠站为例,证实了ClaytonCopula-EVT模型能较好地拟合蚌埠站干旱灾害风险的历史经验分布,计算得出:蚌埠站干旱历时大于5个月,干旱强度超过7.45的极端干旱灾害风险概率为3%,重现期T_∩(t,d)为32.4年,对干旱历时和干旱强度的条件重现期研究得出干旱强度的取值对干旱灾害风险重现期的影响较大。     

基于Copula-ECM-GARCH模型的农产品期货套期保值绩效研究

Copula函数具有可以准确刻画变量间的相依结构、精准描述金融时间序列"尖峰厚尾"分布特点的良好统计性质.针对传统计量模型在计算套期保值比率时存在的局限性,利用Copula函数描述变量的尾部相关性,并结合ECM-GARCH模型,对大豆、小麦、玉米三种国内农产品期货进行套期保值研究,分别计算最优的套期保值比率及其绩效,并与OLS、B-VAR、ECM和ECM-GARCH模型进行比较.结果表明,对于大豆来说,运用Copula-ECM-GARCH模型计算得到的套期保值比率进行对冲操作,可以最大化降低现货市场的价格风险,为投资者提供了一种可以更好规避价格风险的工具选择.     

基于r维正态扩散的区域热带气旋灾害模糊风险分析

从1980-2008年影响广西的热带气旋灾情资料和地面观测资料中选取23组数据,构造灾情指数序列和致灾源指数序列.通过计算得到超越概率的灾害风险估计值.利用r维正态扩散将单值样本扩散为集值样本以构造原始信息矩阵,借助因素空间理论将其转化为模糊关系矩阵,通过模糊近似推理和模糊集重心的计算,得到以致灾源因子为输入样本近似估计灾情的风险值.然后用距离贴近度和择近原则进一步计算和分析致灾因子和承载体易损性的相关程度.最后,计算了各区域灾害的风险度,同时,给出供决策参考的热带气旋灾害风险度区划图.     

Copula函数在水文计算中的适用性分析

论述和探讨了Copula函数在水文计算中的应用及适用性,重点分析了常用的Archimedean CopuIa函数在描述水文变量尾部相关性方面的差异,以及相关系数的不确定性对各Copula函数分析结果的影响,讨论了Copula函数在相关性分析中出现的其他问题及注意事项.     

基于Copula函数和极值理论的金融传染度量——测度美国次贷危机对重要经济体的传染效应

基于Copula函数和极值理论研究美国次贷危机对重要经济体的传染效应,首先根据信息准则来选取Copula函数,然后用Cvm和Ks统计量来检验Copula函数的拟合程度,确保选取合适的Copula函数,并在此基础上计算一般相关系数和尾部相关系数;实证发现使用尾部相关系数度量金融传染并不可靠,因此基于Copula函数和极值理论的POT模型,构造了尾部附近相关系数并通过实证分析了其用于金融传染的有效性.结果表明发达国家所受传染较重,中国所受传染较轻.     

藤Copula模型与多资产投资组合VaR预测

投资组合风险管理往往涉及多个资产,在传统的二元Copula函数面临"维度诅咒"问题及多元Copula函数刻画多变量联合分布时其精确性和灵活性存在各种局限性的情况下,引入藤Copula刻画多个资产收益的联合分布,基于不同的Pair-Copula类别构建藤Copula,运用蒙特卡罗模拟方法计算多资产投资组合的VaR,通过Kupiec和Christoffersen返回检验方法测试藤Copula模型的VaR预测效果,并与传统方差-协方差风险管理方法做比较。实证分析表明,传统的方差-协方差风险管理方法和基于正态Pair-Copula作为藤Copula构建模块的方法不能通过多资产投资组合的VaR预测返回检验;而基于student-t Copula、Clayton Copula具有尾部分布特征的Copula作为构建模块的藤Copula模型能够有效地用于多资产投资组合VaR预测,从而更好的用于指导实践。     

基于藤Copula方法的巨灾风险条件VaR预测

为准确预测巨灾风险的条件VaR,应用藤Copula方法刻画巨灾损失变量间的相关结构,进而得到损失变量间的联合分布和条件分布函数,最终实现对条件VaR的估计.对全球洪水的损失数据进行实证分析,利用核密度估计检验法从常用多元Copula中选出最优的Copula作为比较对象,回测检验结果表明:准确刻画相关结构是精确估计条件VaR的关键,藤Copula方法对巨灾风险条件VaR的预测能力要优于常用多元Copula方法.     

基于最大熵原理的灾害损失分析

灾害以最无序的方式在各地发生,意味着灾害熵达到了极大值.在给定的约束条件下,当灾害熵取极大值时,灾损系列服从P-型分布.灾害损失的重现期指未来某一程度的灾害损失出现的平均时间间隔.根据实测的灾害资料,利用P-型分布函数,计算了未来具有一定重现期的灾害损失大小.这种方法概念明确,便于应用,具有重要的现实意义.     

时变Copula下我国寿险公司投资市场风险经济资本测度

随着保险资金投资渠道的放宽,保险公司对于自身资金运用方面的管理显得日益重要,基于此,选取了国债和政府机构债券、企业债、证券投资基金以及股票这四种资产作为研究对象,将收益率低于同期银行存款利率的情形视为损失,结合样本数据进行了经济资本的测度分析.通过对比以往学者的研究,选定了用GARCH-偏正态分布进行收益率的拟合,并运用时变Copula函数进行风险相关性的测量,计算出了不同置信度下,寿险公司投资市场风险的经济资本.结果显示,时变Copula比常数Copula在风险相关性度量方面表现更好.     

On the principle of maximum entropy and the risk analysis of disaster loss

Disasters that occur everywhere in the most disordered way indicate that disaster entropy has reached the maximum value. Under given constraint conditions, when disaster entropy is the maximum value, the disaster loss series should follow P-III distribution. The occurrence interval of disaster loss refers to the average time interval that disaster loss of certain degree happens in the future. We could, according to the field disaster data and using P-III distribution function, calculate the value of future disaster loss with certain recurrence interval. Explicit in concept and easy to use, such a method has significant meaning in practice.     

基于KMV模型的我国上市公司信用风险研究

在KM V框架的基础上对股权价值计算方法进行了改进,通过改进后的方法,计算出1999年至2006年各年所有上市公司的违约距离、理论违约率、企业价值、股权价值等指标数据.从分析的结果来看,上市公司规模对信用风险有一定影响,上市公司规模越大,信用风险越小,公司规模越小,信用风险越大.从违约风险的变化情况看,2003—2006年上市公司的违约距离呈下降态势,说明近年来上市公司的违约风险加大.对比沪深300上市公司股改前和股改后信用状况,发现股改前后信用状况有显著不同,股改后上市公司的违约风险变大.通过违约距离的敏感性分析,认为股权价值波动率对违约距离最敏感.     

Portfolio selection with a minimax measure in safety constraint

In this paper, we attempt to design a portfolio optimization model for investors who desire to minimize the variation around the mean return and at the same time wish to achieve better return than the worst possible return realization at every time point in a single period portfolio investment. The portfolio is to be selected from the risky assets in the equity market. Since the minimax portfolio optimization model provides us with the portfolio that maximizes (minimizes) the worst return (worst loss) realization in the investment horizon period, in order to safeguard the interest of investors, the optimal value of the minimax optimization model is used to design a constraint in the mean-absolute semideviation model. This constraint can be viewed as a safety strategy adopted by an investor. Thus, our proposed bi-objective linear programming model involves mean return as a reward and mean-absolute semideviation as a risk in the objective function and minimax as a safety constraint, which enables a trade off between return and risk with a fixed safety value. The efficient frontier of the model is generated using the augmented -constraint method on the GAMS software. We simultaneously solve the ratio optimization problem which maximizes the ratio of mean return over mean-absolute semideviation with same minimax value in the safety constraint. Subsequently, we choose two portfolios on the above generated efficient frontier such that the risk from one of them is less and the mean return from other portfolio is more than the respective quantities of the optimal portfolio from the ratio optimization model. Extensive computational results and in-sample and out-of-sample analysis are provided to compare the financial performance of the optimal portfolios selected by our proposed model with that of the optimal portfolios from the existing minimax and mean-absolute semideviation portfolio optimization models on real data from S&P CNX Nifty index.     

沪深股市的相关结构分析与投资组合风险度量——基于ARFIMA-GARCH-Copula模型

金融资产收益率不仅具有尖峰厚尾性、异方差性,还具有长记忆性。基于此,本文建立ARFIMA-GARCH-Copula模型来研究沪深股市的相关结构和等权重投资组合风险值VaR,利用上证指数和深成指数收益率的组合来进行实证研究。首先采用经典R/S分析法检验各个资产收益率的长记忆性,经过分数阶差分后选用GARCH模型建模得到边缘分布。然后选择Copula函数来刻画两资产之间的相关结构,建立联合分布模型。进而采用Monte Carlo方法模拟产生各资产的收益率序列,计算出投资组合的风险值VaR。实证研究表明:沪深股市具有长记忆性,且两者具有对称的尾部相关性;Kupiec检验说明ARFIMA-GARCH-Copula模型较之于GARCH-Copula模型能更准确地度量投资组合风险。     

Two substitutable perishable product disaster inventory systems

A disaster inventory system is considered in which two substitutable items are stored for disaster management. In the event of disaster management, a particular product may become stock-out and the situation warrants that a demand for the particular product during its stock-out period may be substituted with another available similar product in the inventory. From the utility point of view, continuous review inventory models are quite appropriate in disaster inventory management. In this paper, a continuous review two substitutable perishable product disaster inventory model is proposed and analyzed. Since the inventory is maintained for disaster management, an adjustable joint reordering policy for replenishment is adopted. There is no lead time and the replenishment is instantaneous. For this model, some measures of system performance are obtained. The stationary behavior of the model is also considered. Numerical examples are also provided to illustrate the results obtained.     

Dynamic optimal strategy for monitoring disease recurrence

Surveillance to detect cancer recurrence is an important part of care for cancer survivors.In this paper we discuss the design of optimal strategies for early detection of disease recurrence based on each patient’s distinct biomarker trajectory and periodically updated risk estimated in the setting of a prospective cohort study.We adopt a latent class joint model which considers a longitudinal biomarker process and an event process jointly,to address heterogeneity of patients and disease,to discover distinct biomarker trajectory patterns,to classify patients into different risk groups,and to predict the risk of disease recurrence.The model is used to develop a monitoring strategy that dynamically modifies the monitoring intervals according to patients’ current risk derived from periodically updated biomarker measurements and other indicators of disease spread.The optimal biomarker assessment time is derived using a utility function.We develop an algorithm to apply the proposed strategy to monitoring of new patients after initial treatment.We illustrate the models and the derivation of the optimal strategy using simulated data from monitoring prostate cancer recurrence over a 5-year period.