随机连接广义合作网络模型

本文提出了一个项目参与者数T是随机变量的广义合作网络模型,新节点与随机选择的节点合作,通过节点度演化所满足的马尔可夫性,利用马．尔可夫链的方法和技巧得到了度分布的精确解析表达式．并说,明了此广义合作网络不是无标度网络．     

基于MCMC算法的贝叶斯变结构分位自回归模型研究

为了更全面细致的刻画时间序列变结构性的特征及其相依性,提出了一类马尔可夫变结构分位自回归模型。利用非对称Laplace分布构建了模型的似然函数,证明了当回归系数的先验分布选择为扩散先验分布时,参数的各阶后验矩都是存在的,并给出了能确定变点位置和性质的隐含变量的后验完全条件分布。仿真分析结果发现马尔可夫变结构分位自回归模型可以全面有效地实现对时间序列数据变结构性的刻画。并应用贝叶斯Markov分位自回归方法分析了中国证券市场的变结构性,结果发现中国证券市场在不同阶段尾部表现出不同的相依性。     

多元马氏模型Phase-type分布的反问题

本文在多元马尔可夫模型下研究Phase-Type分布的反问题.在确定模型中各随机序列的瞬时状态集转移到吸收态集的首达时间的条件下,根据多元马氏模型的首达时间的条件分布向量序列,针对PhaseType分布的反问题,求出多元马氏模型瞬时状态集的转移概率矩阵.     

二元极值混合模型相关结构的研究

二元极值混合模型由于不能反映极值变量之间的完全相关性,因而在应用上受到了一定的限制,但对适当的相关性仍是一个很好的模型.本文给出了二元极值混合模型的一些基本性质,特别用随机模拟方法研究了对来自其它不同极值copula的随机样本,用混合模型拟合可能产生的影响. 结果表明,如果以Kendallτ表示变量间的相关性,在一定范围内,混合模型能够很好的反映其它模型所具有的相关性,且对渐近独立模型边际参数估计的偏差也不太大.最后应用混合条件分布与GEV条件分布分析英镑对美元和英镑对加元两支汇率日对数回报收益率的风险相关性.     

时长不等数据的vine-copula建模及多资产组合VaR分析

传统的copula模型在对二维以上相依结构建模时存在参数过少的缺陷,vine copula理论基本弥补了这一缺陷.介绍了vine copula理论以及其相对于传统多元模型的优势,尤其提出了vine copula对于时长不一致的数据进行建模具有数据利用率较高的特性,给出了这类数据vine copula的建模步骤以及基于极大似然估计的统计推断.最后对国内A股市场的五种金融股票的联合分布进行建模,并利用蒙特卡罗方法对资产组合的VaR进行了模拟.     

Markov-modulated风险模型破产前最大盈余额与破产赤字的联合分布

应用逐段决定马尔可夫过程理论及补充变量技巧,使Markov-modulated风险过程成为齐次强马尔可夫过程,然后利用强马氏性及首达时间分布给出了其破产前最大盈余额与破产赤字的联合分布.     

基于Copula函数的应力-强度模型可靠度的非参数估计

本文研究了相关的应力变量和强度变量在右删失的情形下,应力-强度模型可靠度的非参数估计.其中变量之间的相关关系采用常见的Farlie-Gurnbel-Morgenstern copula函数和Clayton copula函数来度量.采用经验过程的理论,本文建立了所提出估计量的相合性及渐近正态性.数值模拟的结果表明所提出的方法在有限样本下表现良好.本文所提出的方法在实际中有广泛的应用前景.     

双模冗余非马尔可夫模型可修系统分析

文章采用补充变量, 将双模冗余系统的非马尔可夫模型转化为马尔可夫过程模型, 针对该模型进行可靠性估计, 比较了不计维修时系统的寿命分布, 介绍了快修条件下系统的可靠性工作特点.牵引变压器应用研究表明这种分析方法是十分有效的.     

改进的pair-copula参数估计方法在经济研究中的应用

对于pair-copula中的参数估计,大多假设copula函数的参数和条件变量独立,将参数简化成一个不依赖于条件变量的常数.本文假设copula函数的参数和条件变量不独立,该参数是以条件变量为自变量的一元函数.应用该方法实证分析了“克强指数”三个指标铁路货运量、工业用电量和贷款发放量的对数增长率之间的关系,研究发现该方法优于简化的pair-copula参数估计,并且得出在固定铁路货运量不变时,工业用电量和银行贷款发放量成负相关关系,且这种负相关性随铁路货运量增加而减弱.     

基于pair-copula情景生成和广义熵约束的CVaR投资组合模型研究

通过GARCH模型对收益率序列的边缘分布建模,结合copula构建收益率的联合分布函数,并由蒙特卡洛模拟生成收益率的情景,得到的结果代入广义熵约束的CVaR模型中,由此得到最优的投资权重.实证表明,在考虑不同资产之间的相依结构基础上得到的最优化结果相比传统的M-V模型具有明显的优势,在分散化和收益性上的到很好的效果.     

<Emphasis Type="Italic">k</Emphasis>th-order Markov extremal models for assessing heatwave risks

Heatwaves are defined as a set of hot days and nights that cause a marked short-term increase in mortality. Obtaining accurate estimates of the probability of an event lasting many days is important. Previous studies of temporal dependence of extremes have assumed either a first-order Markov model or a particularly strong form of extremal dependence, known as asymptotic dependence. Neither of these assumptions is appropriate for the heatwaves that we observe for our data. A first-order Markov assumption does not capture whether the previous temperature values have been increasing or decreasing and asymptotic dependence does not allow for asymptotic independence, a broad class of extremal dependence exhibited by many processes including all non-trivial Gaussian processes. This paper provides a kth-order Markov model framework that can encompass both asymptotic dependence and asymptotic independence structures. It uses a conditional approach developed for multivariate extremes coupled with copula methods for time series. We provide novel methods for the selection of the order of the Markov process that are based upon only the structure of the extreme events. Under this new framework, the observed daily maximum temperatures at Orleans, in central France, are found to be well modelled by an asymptotically independent third-order extremal Markov model. We estimate extremal quantities, such as the probability of a heatwave event lasting as long as the devastating European 2003 heatwave event. Critically our method enables the first reliable assessment of the sensitivity of such estimates to the choice of the order of the Markov process.     

A copula-based model of speculative price dynamics in discrete time

This paper suggests a new technique to construct first order Markov processes using products of copula functions, in the spirit of Darsow et al. (1992) [10]. The approach requires the definition of (i) a sequence of distribution functions of the increments of the process, and (ii) a sequence of copula functions representing dependence between each increment of the process and the corresponding level of the process before the increment. The paper shows how to use the approach to build several kinds of processes (stable, elliptical, Farlie-Gumbel-Morgenstern, Archimedean and martingale processes), and how to extend the analysis to the multivariate setting. The technique turns out to be well suited to provide a discrete time representation of the dynamics of innovations to financial prices under the restrictions imposed by the Efficient Market Hypothesis.     

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Credit valuation adjustment is the price adjustment of financial contract considering possible default of counterparty and it is an important way to measure counterparty risk. It is the key to establish a reasonable default dependence structure model. We introduce an economic state variable and shot noise processes in a Markov copula model and establish a regime switching Markov copula model with shot noise, where we can not only describe the impact of common economic conditions characteristics but also describe the credit name's characteristic. In this proposed model, we study martingale property of the model and the collateralized CVA of credit default swaps, and furthermore, we perfer some numerical calculations on the collateralized CVA and examine the impact of some model parameters on the CVA.     

Graphical modelling of multivariate time series

We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series with non-linear dependences. The models are derived from ordinary time series models by imposing constraints that are encoded by mixed graphs. In these graphs each component series is represented by a single vertex and directed edges indicate possible Granger-causal relationships between variables while undirected edges are used to map the contemporaneous dependence structure. We introduce various notions of Granger-causal Markov properties and discuss the relationships among them and to other Markov properties that can be applied in this context. Examples for graphical time series models include nonlinear autoregressive models and multivariate ARCH models.     

COPAR—multivariate time series modeling using the copula autoregressive model

The analysis of multivariate time series is a common problem in areas like finance and economics. The classical tools for this purpose are vector autoregressive models. These however are limited to the modeling of linear and symmetric dependence. We propose a novel copula‐based model that allows for the non‐linear and non‐symmetric modeling of serial as well as between‐series dependencies. The model exploits the flexibility of vine copulas, which are built up by bivariate copulas only. We describe statistical inference techniques for the new model and discuss how it can be used for testing Granger causality. Finally, we use the model to investigate inflation effects on industrial production, stock returns and interest rates. In addition, the out‐of‐sample predictive ability is compared with relevant benchmark models. Copyright © 2014 John Wiley & Sons, Ltd.     

Crisis and risk dependencies

The knowledge of the multivariate stochastic dependence between the returns of asset classes is of importance for many finance applications, such as asset allocation or risk management. By means of goodness-of-fit tests, we analyze for a multitude of portfolios consisting of different asset classes whether the stochastic dependence between the portfolios’ constituents can be adequately described by multivariate versions of some standard parametric copula functions. Furthermore, we test whether the stochastic dependence between the returns of different asset classes has changed during the recent financial crisis. The main findings are: First, whether a specific copula assumption can be rejected or not, crucially depends on the asset class and the time period considered. Second, different goodness-of-fit tests for copulas can yield very different results and these differences can vary for different asset classes and for different tested copulas. Third, even when using various goodness-of-fit tests for copulas, it is not always possible to differentiate between various copula assumptions. Fourth, during the financial crisis, copula assumptions are more frequently rejected. However, the results also raise some concerns over the suitability of goodness-of-fit tests for copulas as a diagnostic tool for identifying stressed risk dependencies.     

Tensor Approximation of Generalized Correlated Diffusions and Functional Copula Operators

In this paper we develop a class of applied probabilistic continuous time but discretized state space decompositions of the characterization of a multivariate generalized diffusion process. This decomposition is novel and, in particular, it allows one to construct families of mimicking classes of processes for such continuous state and continuous time diffusions in the form of a discrete state space but continuous time Markov chain representation. Furthermore, we present this novel decomposition and study its discretization properties from several perspectives. This class of decomposition both brings insight into understanding locally in the state space the induced dependence structures from the generalized diffusion process as well as admitting computationally efficient representations in order to evaluate functionals of generalized multivariate diffusion processes, which is based on a simple rank one tensor approximation of the exact representation. In particular, we investigate aspects of semimartingale decompositions, approximation and the martingale representation for multidimensional correlated Markov processes. A new interpretation of the dependence among processes is given using the martingale approach. We show that it is possible to represent, in both continuous and discrete space, that a multidimensional correlated generalized diffusion is a linear combination of processes originated from the decomposition of the starting multidimensional semimartingale. This result not only reconciles with the existing theory of diffusion approximations and decompositions, but defines the general representation of infinitesimal generators for both multidimensional generalized diffusions and, as we will demonstrate, also for the specification of copula density dependence structures. This new result provides immediate representation of the approximate weak solution for correlated stochastic differential equations. Finally, we demonstrate desirable convergence results for the proposed multidimensional semimartingales decomposition approximations.     

Copula-Type Estimators for Flexible Multivariate Density Modeling Using Mixtures

Copulas are popular as models for multivariate dependence because they allow the marginal densities and the joint dependence to be modeled separately. However, they usually require that the transformation from uniform marginals to the marginals of the joint dependence structure is known. This can only be done for a restricted set of copulas, for example, a normal copula. Our article introduces copula-type estimators for flexible multivariate density estimation which also allow the marginal densities to be modeled separately from the joint dependence, as in copula modeling, but overcomes the lack of flexibility of most popular copula estimators. An iterative scheme is proposed for estimating copula-type estimators and its usefulness is demonstrated through simulation and real examples. The joint dependence is modeled by mixture of normals and mixture of normal factor analyzer models, and mixture of t and mixture of t-factor analyzer models. We develop efficient variational Bayes algorithms for fitting these in which model selection is performed automatically. Based on these mixture models, we construct four classes of copula-type densities which are far more flexible than current popular copula densities, and outperform them in a simulated dataset and several real datasets. Supplementary material for this article is available online.     

多元Copula-GARCH模型及其在金融风险分析上的应用

针对传统风险分析模型的不足,结合Copula技术和GARCH模型,提出了多元Copula-GARCH模型。指出该模型不仅可以捕捉金融市场间的非线性相关性,还可以得到更灵活的多元分布进而用于资产投资组合VaR分析。在详细探讨了基于Copula技术的资产投资组合的MonteCarlo仿真技术的基础上,运用具有不同边缘分布的多元Copula-GARCH模型,对上海股市进行了研究,结果证实了所提模型和方法的可行性和有效性。     

A generalized beta copula with applications in modeling multivariate long-tailed data

This work proposes a new copula class that we call the MGB2 copula. The new copula originates from extracting the dependence function of the multivariate GB2 distribution (MGB2) whose marginals follow the univariate generalized beta distribution of the second kind (GB2). The MGB2 copula can capture non-elliptical and asymmetric dependencies among marginal coordinates and provides a simple formulation for multi-dimensional applications. This new class features positive tail dependence in the upper tail and tail independence in the lower tail. Furthermore, it includes some well-known copula classes, such as the Gaussian copula, as special or limiting cases.To illustrate the usefulness of the MGB2 copula, we build a trivariate MGB2 copula model of bodily injury liability closed claims. Extended GB2 distributions are chosen to accommodate the right-skewness and the long-tailedness of the outcome variables. For the regression component, location parameters with continuous predictors are introduced using a nonlinear additive function. For comparison purposes, we also consider the Gumbel and t copulas, alternatives that capture the upper tail dependence. The paper introduces a conditional plot graphical tool for assessing the validation of the MGB2 copula. Quantitative and graphical assessment of the goodness of fit demonstrate the advantages of the MGB2 copula over the other copulas.