Dependence tree structure estimation via copula

We propose an approach for dependence tree structure learning via copula. A nonparametric algorithm for copula estimation is presented. Then a Chow-Liu like method based on dependence measure via copula is proposed to estimate maximum spanning bivariate copula associated with bivariate dependence relations. The main advantage of the approach is that learning with empirical copula focuses on dependence relations among random variables, without the need to know the properties of individual variables as well as without the requirement to specify parametric family of entire underlying distribution for individual variables. Experiments on two real-application data sets show the effectiveness of the proposed method.     

需求依赖于价格情境下基于Copula-CVaR 的报童决策

探讨价格不确定下,需求-价格相关性与风险态度对决策行为的影响.建立随机需求与随机价格相关情境下基于Copula-CVaR的报童决策模型,Copula函数描述相关性,条件风险价值(CVaR)反映风险态度,证明了模型解的存在性和惟一性.蒙特卡罗模拟发现,需求与价格的相关性与风险态度对决策的交互作用使决策行为发生规律性变化,决策者对价格波动有一定容忍度,需求与价格相关性趋于不相关与完全负相关时市场趋于同质性.     

Robust estimators and tests for bivariate copulas based on likelihood depth

Estimators and tests based on likelihood depth for one-parametric copulas are given. For the Gaussian and Gumbel copulas, it is shown that the maximum depth estimators are biased. They can be corrected and the new estimators are robust against contamination. For testing, simplicial likelihood depth is considered. Because of the bias of the maximum depth estimator, simplicial likelihood depth is not a degenerated U-statistic so that easily asymptotic α-level tests can be derived for arbitrary hypotheses. Tests are in particular investigated for the one-sided alternatives. Simulation studies for the Gaussian and Gumbel copulas show that the power of the first test is rather good, but the latter one has to be improved, which is also done here. The new tests are robust against contamination.     

香港沿岸台风暴潮灾害联合强度概率分析

以香港东部鲗鱼涌和大埔滘两个验潮站的风暴增水数据为基础,以1999-2018年影响香港的台风过程所引发的风暴最大增水为研究对象,利用广义极值分布分别对两站的最大台风增水进行一元拟合,并基于二元Copula函数,构造两站最大台风增水的联合概率分布,根据其联合重现频率进行潮灾的联合强度概率分析。研究结果表明:两站台风暴潮最大增水变量的联合重现频次能够反映台风在香港东部引发的风暴潮的强度,这种联合概率分析较一元分析有更强的地区适用性。     

变化环境下的治涝效益估算方法研究

治涝工程直接经济效益表现在涝灾的减免程度上，应该只是因有、无治涝工程措施而导致的涝灾损失的差值。由于在治涝前、后，涝区的内环境常常可能会发生变化，承灾体的种类、数量和空间分布也都可能会发生变化，因此，变化环境下治涝工程效益应该是有治涝工程情况下比假设无该治涝工程情况下减少的涝灾损失；而且孕灾外环境可能是随机变化的，故各频率的暴雨导致的涝灾损失应为与各种承泄区水位组合下的涝灾损失的数学期望值。因此，现有的治涝效益估算方法均不能或不完全适用于变化环境下的治涝效益估算。本文基于Copula函数和GIS构建的变化环境下治涝效益分析计算模型，用Copula函数构建涝区暴雨和承泄区水位的联合分布，借助GIS技术构建涝区数字高程模型。根据涝区暴雨和承泄区水位遭遇组合下的积水过程估算其涝灾损失，进而计算有治涝工程和假设无该治涝工程两种工况时所有组合下的涝灾损失期望值，从而得到治涝工程效益。并以实际案例来进行研究分析。     

A New Approach for Firm Value and Default Probability Estimation beyond Merton Models

In this paper we present a new model to assess the firm value and the default probability by using a bivariate contingent claim analysis and copula theory. First we discuss an unfeasible case, given the current derivative market on corporate bonds, which involves univariate digital options to compute the risk neutral probabilities. We then discuss a feasible model, which considers risky interest rates, instead. Moreover, we develop in this framework a new methodology to extract default probabilities from stock prices, only, going beyond the standard KMV-Merton model. Besides, the non-observability of the Merton model’s state variable requires numerical methods, but the results can be unstable with noisy risky data. We show how the null price can be used as a useful barrier to separate an operative firm from a defaulted one, and to estimate its default probability. We then present an empirical application with both operative and defaulted firms to show the advantages of our approach.      

南水北调西线工程水源区河流与黄河的丰枯遭遇分析

针对目前二维联合分布模型不能同时分析多条河流的丰枯遭遇特性，运用四元Copula连接函数构造了鲜水河、足木足河、绰斯甲河以及黄河上游兰州水文站天然径流系列的四维联合分布，研究了南水北调西线工程水源区河流与受水区黄河上游的丰枯遭遇问题。结果表明，如果不考虑黄河上游兰州水文站丰与水源区河流非全枯的组合，则有利于调水的丰枯遭遇频率为43.8%；如果把兰州水文站丰、水源区河流非全枯的组合考虑进来，有利于调水的丰枯遭遇频率可达77.8%，即调水河流之间能进行补偿调度的概率比较大，这对南水北调西线工程的实施是非常有利的     

On copulas and their diagonals

We formulate the necessary and sufficient conditions for a function δ:[0,1]→[0,1] to be the diagonal section of a multivariate absolutely continuous copula. Moreover we provide some simple analytic formulas for copulas having given diagonal section or given distribution functions of order statistics.     

基于Copula函数的郑州市夏季双重城市热岛及其影响因素关系分析

城市热环境变化影响城市小区域气候,探究影响因子与其作用机制,可有效减缓城市热岛现象。利用郑州市1960～2017年长序列数据,从相对热岛（RHI）和绝对热岛（AHI）两个层面探究驱动因子降雨（R）、蒸发（E）、建成区面积(B_BUA)、城镇化率(U_UR)的影响关系,利用交叉小波和小波相干探究热岛与降雨的雨热关系,采用Copula函数计算影响因子在不同取值条件下与热岛的遭遇概率。结果表明,相对热岛-相对降雨在短中周期、绝对热岛-降雨在短周期上均呈负相关关系,雨热关系不同步,且绝对热岛-降雨的关系最为显著;影响因子B_BUA、U_UR取值越大,R取值越小,则与RHI、AHI的遭遇概率越大;不同影响因子在不同评价层面,敏感性强弱不同,E在不同层面的反馈机制也不同,可见选取合适评价分析层面,有利于准确量化影响程度。     

基于Copula函数的甬江流域雨潮遭遇组合分析

雨潮遭遇组合分析和组合方式的选取是沿海地区防洪治涝规划的重要内容之一。以甬江流域为例,在考虑尾部相关性的基础上,采用Gumbel Copula函数构建流域暴雨和河口潮位的联合概率分布,分析不同暴雨潮位组合下的同现风险率、条件风险率和组合风险率,并基于条件最可能组合原理,计算给定设计暴雨条件下潮位的条件最可能值和置信区间。结果表明,当甬江流域发生10、20、50、100年一遇暴雨时,相应镇海站最可能发生4、8、21、43年一遇潮位。