系统性风险度量CoES的建模和检验

本文结合极值理论(Extreme Value Theory,EVT)和新的动态混合Copula(Dynamic Mixture Copula,DM-Copula)函数,提出了一种新的CoES估计方法DM-Copula-EVT。在EVT建模中,本文改进了阈值的选取方法以避免选择的主观性,并提出了一系列新的动态混合Copula以更好地刻画金融市场日益复杂的尾部关联性。此外,本文首次提出了检验CoES模型设定正确性的后验分析方法,包括无条件覆盖性检验和条件覆盖性检验。将本文建模和检验方法应用于我国金融市场,研究发现:相对于传统使用的t分布,EVT能更好地拟合指数的尾部分布;新的动态混合Copula函数能更好地刻画金融部门与系统之间的复杂关联性。     

Property of bivariate poisson distribution and its application to stochastic processes

Assuming that the random vectors X ₁ and X ₂ have independent bivariate Poisson distributions, the conditional distribution of X ₁ given X ₁?+?X ₂?=?n is obtained. The conditional distribution turns out to be a finite mixture of distributions involving univariate binomial distributions and the mixing proportions are based on a bivariate Poisson (BVP) distribution. The result is used to establish two properties of a bivariate Poisson stochastic process which are the bivariate extensions of the properties for a Poisson process given by Karlin, S. and Taylor, H. M. (1975). A First Course in Stochastic Processes, Academic Press, New York.     

On the distribution of quotient of random variables conditioned to the positive quadrant

Abstract

Motivated by Caginalp and Caginalp [Physica A—Statistical Mechanics and Its Applications, 499, 2018, 457–471], we derive the exact distribution of X/Y conditioned on X?>?0, Y?>?0 for more than ten classes of distributions, including the bivariate t, bivariate Cauchy, bivariate Lomax, Arnold and Strauss’ bivariate exponential, Balakrishna and Shiji’s bivariate exponential, Mohsin et al.’s bivariate exponential, Morgenstern type bivariate exponential, bivariate gamma exponential and bivariate alpha skew normal distributions. The results can be useful in finance and other areas.     

Failure Inference and Optimization for Step Stress Model Based on Bivariate Wiener Model

In this article, we consider the situation under a life test, in which the failure time of the test units are not related deterministically to an observable stochastic time varying covariate. In such a case, the joint distribution of failure time and a marker value would be useful for modeling the step stress life test. The problem of accelerating such an experiment is considered as the main aim of this article. We present a step stress accelerated model based on a bivariate Wiener process with one component as the latent (unobservable) degradation process, which determines the failure times and the other as a marker process, the degradation values of which are recorded at times of failure. Parametric inference based on the proposed model is discussed and the optimization procedure for obtaining the optimal time for changing the stress level is presented. The optimization criterion is to minimize the approximate variance of the maximum likelihood estimator of a percentile of the products’ lifetime distribution.     

BAYESIAN ANALYSIS FOR THE SUPERPOSITION OF TWO DEPENDENT NONHOMOGENEOUS POISSON PROCESSES

ABSTRACT

A Bayesian analysis for the superposition of two dependent nonhomogenous Poisson processes is studied by means of a bivariate Poisson distribution. This particular distribution presents a new likelihood function which takes into account the correlation between the two nonhomogenous Poisson processes. A numerical example using Markov Chain Monte Carlo method with data augmentation is considered.     

On a bivariate Kumaraswamy type exponential distribution

ABSTRACT

This paper considers a class of absolutely continuous bivariate exponential distributions whose univariate margins are the ordinary exponential distributions. We study different mathematical properties of the proposed model. The estimation of the parameters by maximum likelihood is discussed. Application is made to a real data example to illustrate the flexibility of theproposed distribution for data analysis.     

A bivariate extension of the beta generated distribution derived from copulas

In this paper, we introduce a new class of bivariate distributions whose marginals are beta-generated distributions. Copulas are employed to construct this bivariate extension of the beta-generated distributions. It is shown that when Archimedean copulas and convex beta generators are used in generating bivariate distributions, the copulas of the resulting distributions also belong to the Archimedean family. The dependence of the proposed bivariate distributions is examined. Simulation results for beta generators and an application to financial risk management are presented.     

Use of approximate bayesian methods for the block and basu bivariate exponential distribution

Summary In this paper, we present a Bayesian analysis of the bivariate exponential distribution of Block and Basu (1974) assuming different prior densities for the parameters of the model and considering Laplace's method to obtain approximate marginal posterior and posterior moments of interest. We also find approximate Bayes estimators for the reliability of two-component systems at a specified timet ₀ considering series and parallel systems. We illustrate the proposed methodology with a generated data set.     

金融机构尾部风险溢出效应———基于改进非对称CoVaR模型的研究

为准确度量我国金融机构对金融系统的尾部风险溢出,本文改进了基于CoVaR 方法的分位数回归模型。基于极值理论和ARMA-GARCH模型拟合收益率边缘分布,构建了改进的非对称CoVaR模型,从系统性金融风险贡献绝对值(△CoVaR)和相对值(%CoVaR)两方面详细考察了2002年7月1日至2018年12月28日我国42家上市金融机构的尾部风险溢出效应。结果表明:在q=0.01的情况下,不同类型金融机构对金融市场的系统性金融风险贡献有显著差异,银行类与保险类机构的系统性金融风险值得重点关注;金融机构的系统性金融风险贡献相对值与在险价值存在显著联系,自身风险最低的银行类机构具有最大的风险溢出强度,是我国系统性金融风险防范的核心对象,尤其是国有控股银行。研究结论对于有效防范我国系统性金融风险具有重要的理论价值和现实意义。     

Nonparametric estimation of the bivariate survival function with left-truncated and right-censored data

In this note, we consider estimating the bivariate survival function when both components are subject to left truncation and right censoring. We propose two types of estimators as generalizations of the Dabrowska and Campbell and Földes estimators. The consistency of the proposed estimators is established. A simple bootstrap method is used for obtaining precision estimation of the proposed estimators. A simulation study is conducted to investigate the performance of the proposed estimators.     

Approximation of the Bivariate Renewal Function

Recently, Kambo and his co-researchers (2012) proposed a method of approximation for evaluating the one-dimensional renewal function based on the first three moments. Their method is simple and elegant, which gives exact values for well-known distributions. In this article, we propose an analogous method for the evaluation of bivariate renewal function based on the first two moments of the variables and their joint moment. The proposed method yields exact results for certain widely used bivariate distributions like bivariate exponential distribution, bivariate Weibull distributions, and bivariate Pareto distributions. An illustrative example in the form of a two-dimensional warranty problem is considered and comparisons of our method are made with the results of other models.     

The finite-time ruin probability of a discrete-time risk model with GARCH discounted factors and dependent risks

The finite-time ruin probability of a discrete-time risk model with dependent stochastic discount factors and dependent insurance and financial risks is investigated in this paper. Assume that the stochastic discount factors follow a GARCH process and the one-period insurance and financial risks form a sequence of independent and identically distributed random pairs, which are the copies of a random pair with a bivariate Sarmanov dependent distribution. When the common distribution of claim-sizes is heavy-tailed, we establish an asymptotic estimate for the finite-time ruin probability. Applying the result to a special case, we also get conservative asymptotic bounds. A numerical simulation is given at the end of the paper.     

Preservation of dependence concepts under bivariate weighted distributions

ABSTRACT

In this paper, we provide conditions under which some bivariate dependence structures are preserved under bivariate weighted distributions. Bivariate weighted distributions whose dependence structure is the same as the original distribution are characterized. Finally, we discuss some examples to show the usefulness of our results.     

On bivariate transformation of scale distributions

ABSTRACT

Elsewhere, I have promoted (univariate continuous) “transformation of scale” (ToS) distributions having densities of the form 2g(Π^?1(x)) where g is a symmetric distribution and Π is a transformation function with a special property. Here, I develop bivariate (readily multivariate) ToS distributions. Univariate ToS distributions have a transformation of random variable relationship with Azzalini-type skew-symmetric distributions; the bivariate ToS distribution here arises from marginal variable transformation of a particular form of bivariate skew-symmetric distribution. Examples are given, as are basic properties—unimodality, a covariance property, random variate generation—and connections with a bivariate inverse Gaussian distribution are pointed out.     

On the estimation of extreme directional multivariate quantiles

Abstract

In multivariate extreme value theory (MEVT), the focus is on analysis outside of the observable sampling zone, which implies that the region of interest is associated to high risk levels. This work provides tools to include directional notions into the MEVT, giving the opportunity to characterize the recently introduced directional multivariate quantiles (DMQ) at high levels. Then, an out-sample estimation method for these quantiles is given. A bootstrap procedure carries out the estimation of the tuning parameter in this multivariate framework and helps with the estimation of the DMQ. Asymptotic normality for the proposed estimator is provided and the methodology is illustrated with simulated data-sets. Finally, a real-life application to a financial case is also performed.     

Bivariate inverse Weibull distribution

ABSTRACT

Recently it is observed that the inverse Weibull (IW) distribution can be used quite effectively to analyse lifetime data in one dimension. The main aim of this paper is to define a bivariate inverse Weibull (BIW) distribution so that the marginals have IW distributions. It is observed that the joint probability density function and the joint cumulative distribution function can be expressed in compact forms. Several properties of this distribution such as marginals, conditional distributions and product moments have been discussed. We obtained the maximum likelihood estimates for the unknown parameters of this distribution and their approximate variance– covariance matrix. We perform some simulations to see the performances of the maximum likelihood estimators. One data set has been re-analysed and it is observed that the bivariate IW distribution provides a better fit than the bivariate exponential distribution.     

Graphical Network Models for International Financial Flows

The late-2000s financial crisis stressed the need to understand the world financial system as a network of countries, where cross-border financial linkages play a fundamental role in the spread of systemic risks. Financial network models, which take into account the complex interrelationships between countries, seem to be an appropriate tool in this context. To improve the statistical performance of financial network models, we propose to generate them by means of multivariate graphical models. We then introduce Bayesian graphical models, which can take model uncertainty into account, and dynamic Bayesian graphical models, which provide a convenient framework to model temporal cross-border data, decomposing the model into autoregressive and contemporaneous networks. The article shows how the application of the proposed models to the Bank of International Settlements locational banking statistics allows the identification of four distinct groups of countries, that can be considered central in systemic risk contagion.     

Stochastic EM algorithm of a finite mixture model from hurdle Poisson distribution with missing responses

ABSTRACT

In this article, a finite mixture model of hurdle Poisson distribution with missing outcomes is proposed, and a stochastic EM algorithm is developed for obtaining the maximum likelihood estimates of model parameters and mixing proportions. Specifically, missing data is assumed to be missing not at random (MNAR)/non ignorable missing (NINR) and the corresponding missingness mechanism is modeled through probit regression. To improve the algorithm efficiency, a stochastic step is incorporated into the E-step based on data augmentation, whereas the M-step is solved by the method of conditional maximization. A variation on Bayesian information criterion (BIC) is also proposed to compare models with different number of components with missing values. The considered model is a general model framework and it captures the important characteristics of count data analysis such as zero inflation/deflation, heterogeneity as well as missingness, providing us with more insight into the data feature and allowing for dispersion to be investigated more fully and correctly. Since the stochastic step only involves simulating samples from some standard distributions, the computational burden is alleviated. Once missing responses and latent variables are imputed to replace the conditional expectation, our approach works as part of a multiple imputation procedure. A simulation study and a real example illustrate the usefulness and effectiveness of our methodology.     

A bivariate mixture of negative binomial distributions and its applications

Abstract

We construct a new bivariate mixture of negative binomial distributions which represents over-dispersed data more efficiently. This is an extension of a univariate mixture of beta and negative binomial distributions. Characteristics of this joint distribution are studied including conditional distributions. Some properties of the correlation coefficient are explored. We demonstrate the applicability of our proposed model by fitting to three real data sets with correlated count data. A comparison is made with some previously used models to show the effectiveness of the new model.     

Estimation of bivariate and marginal distributions with censored data

Summary. Consider a pair of random variables, both subject to random right censoring. New estimators for the bivariate and marginal distributions of these variables are proposed. The estimators of the marginal distributions are not the marginals of the corresponding estimator of the bivariate distribution. Both estimators require estimation of the conditional distribution when the conditioning variable is subject to censoring. Such a method of estimation is proposed. The weak convergence of the estimators proposed is obtained. A small simulation study suggests that the estimators of the marginal and bivariate distributions perform well relatively to respectively the Kaplan–Meier estimator for the marginal distribution and the estimators of Pruitt and van der Laan for the bivariate distribution. The use of the estimators in practice is illustrated by the analysis of a data set.