动态贝叶斯信用评级的宏观经济冲击模型

本文考虑了宏观经济金融指标和潜在的系统性冲击,提出了动态评价信用质量的贝叶斯模型,以处理在债券信用风险量化中存在的样本量较小和违约事件稀疏问题。模型的动态特征可以解释相同信用等级在不同时期的违约概率之间的相关性,模型中宏观协变量可以解释宏观经济状况对债券市场信用质量的影响,潜在冲击项可以解释在给定时期内的不同等级的转移概率之间的相依性。利用2009年到2018年中国债券市场上相关债券的财务、非财务和历史评级数据对模型进行了实证检验。结果表明模型能够有效的估计低违约组合的非零违约概率,可以解释宏观经济变量和潜在冲击对不同等级债券的影响力,以及信用等级转移中存在的相依性。模型可以为监管部门、评级机构和债券投资者提供一个新的模型选择思路。     

基于投影寻踪和最优分割的企业信用评级模型

提出一种基于投影寻踪和最优分割的企业信用评级模型。该模型运用投影寻踪对样本企业进行信用综合评分,将信用综合得分由大到小排序,生成有序样品序列;利用最优分割法对有序样品进行聚类,得出明确的聚类结果;将最优分割点对应的信用综合得分作为划分信用等级的阈值,从而实现对样本企业的信用评级。应用实例证明了该模型的可行性和有效性。     

基于信息增益的小型工业企业信用评级模型

信用评级就是衡量一笔债务违约的可能性,评价债务违约风险的大小。本文利用信息增益方法建立了信用评级模型,并以小型工业企业贷款数据为对象进行了实证分析。本文的创新与特色:一是按照指标的信息增益越大、越能将违约与非违约企业区分出来的思路,筛选出对违约状态有较大影响的指标。改变了现有研究不以违约鉴别力作为指标遴选标准的不足。二是在相关程度高的一对冗余指标中,删除信息增益小、即违约鉴别能力差的指标,既避免指标间反映信息重复,又避免误删违约鉴别能力强的指标。三是利用信息增益值对指标进行赋权,保证违约鉴别能力越大的指标赋予的权重越大。改变了现有研究赋权不反映指标的违约鉴别能力大小的弊端。实证结果表明:本文遴选的包括资产负债率、行业景气指数、抵质押担保等31个指标对违约状态有显著的鉴别能力,且反映信息不重复。偿债能力是影响小型工业企业信用评级的关键要素。     

基于平滑扩充原理的商业银行信用风险评级模型及实证

本文通过银行的资产质量方面、资本充足率方面、管控效能层面、盈利状态层面、流动性层面与社会敏感度层面等构建商业银行信用风险评价体系。根据平滑扩充原理模拟生成大样本数据,对评级得分进行扩充,进而根据扩充后的大样本数据划分银行的信用风险等级。解决了由于样本少、无法对信用等级合理划分的难题。通过实证分析可以了解到,本文得出的银行评级信息和标准普尔提供的评价结论存在共同的序关系状态。因此,可根据本模型对大多数未经过国际权威机构评级的银行进行风险评级。     

基于Group-LASSO方法的广义半参数可加信用评分模型应用研究

信用风险是目前商业银行面临的风险中最为重要和最为复杂的,新巴塞尔协议要求各国条件的银行通过实施内部评级法来度量并控制信用风险,内部评级法即通过银行收集的客户相历史数据来构建数学模型,测算客户的违约概率进而对客户进行评分。文章针对信用评分模型解释变量维数较高,类型丰富,好坏客户类型数量不均衡等特点,利用广义半参数可加模型对户违约概率进行建模,并将Group LASSO方法应用于模型进行变量选择和估计。实证研究表明本文提出的模型和方法与以往常用的线性logistic回归模型相比,在模型的判别能力和预测能以及解释性和计算效率上均有较大优势。     

信用评级模型的特征选择方法研究

特征选择是信用评级建模的重要环节,合理的特征选择能够简化模型结构和提升分类效果.借鉴w-L1SVM模型的加权思想,借助Logistic-Group-Lasso模型筛选组变量的优势,提出处理信用评级特征选择问题的加权Logistic-GroupLasso(w-LGL)模型,该模型在选择变量时更加关注误判成本较高的违约客户,且能够实现分类变量的整组处理.与常规特征选择方法相比,w-LGL模型在数值模拟与实证研究中的分类效果更好.     

基于混合式SMOTE和RF模型的小额贷款公司客户信用风险研究

小额借贷中的个人信用风险问题持续制约着小额贷款行业的健康可持续发展。针对小贷公司在进行信用风险评估时对高违约风险客户识别准确率较低的难题,运用混合式SMOTE、RF算法来同时处理业务数据中高维、非均衡两个问题。本文借助江苏J小贷公司的实例数据,依次构建随机森林(Random Forest, RF)模型、SMOTE-RF模型以及Borderline-SMOTE-RF模型并进行模型测试;再选用SVM算法进行对比实验以此衡量模型的信用风险评价精度。随后基于模型对于指标重要性的评分筛选出6项指标作为影响个人信用风险的关键指标。实验证明基于Borderline-SMOTE-RF算法对于小额贷款个人信用风险评价模型的分类性能最佳;在筛选关键指标时,为避免人工合成虚拟样本对指标重要性影响,需要结合三类模型评分进行综合选择。     

信用评级模型的数据离散化研究

连续变量离散化属于信用评级建模的初始阶段,科学的离散化操作能够提升模型的分类效果和参数的稳定性,便于评级模型的产品呈现.考虑信用评级的误判成本差异,对类别-属性一致性最大化准则进行类别权重调整,提出ACACM准则,并提出基于ACACM准则的数据离散化算法.ACACM算法调整原算法中不同类别个体的权重,更加倾向于刻画误判成本较高的违约客户,使离散化后的变量能够提升评级模型的风险控制能力,更适合信用评级建模.     

处理不平衡征信数据的零膨胀信用评级模型

征信数据中的客户往往呈现"好多坏少"的不平衡结构,这种结构使得一般的分类模型在预测客户信用表现时失效。本文基于零膨胀计数模型的建模思想,分别提出处理因变量为二分类变量、多分类变量、计数变量的零膨胀信用评级模型(ZICSM),将客户结构拆分为稳定好客户、不稳定好客户和坏客户三个部分,利用模型自身优势形成严谨和宽松的两套贷款审批机制。ZICSM模型对目标函数进行权数调整,使模型更加关注"坏"客户,在目标函数中加入惩罚项,使模型具备组变量选择功能。此外,本文提出兼顾风险把控和市场份额的RS得分指标,借以评价信用评级模型的分类效果。模拟研究和实证研究的结果表明,ZICSM模型能够提升金融机构的贷款收益,增加其审批机制的灵活性,适用于处理征信数据的不平衡问题。     

区间直觉模糊信息下的监理工程师信用评价

由于外界环境的复杂多变和决策者的主观偏好,若运用传统信用评价方法单从业主或承包商的视角对监理工程师进行信用评价,会导致评价结果出现偏差。针对此本文从利益相关者的层面,运用区间直觉模糊集构建模糊综合评价模型,对监理工程师的信用行为进行评价,此模型通过相似性度量值、精确度函数分别得到利益相关者的权重和信用评价指标的权重,并在此基础上运用IIFHG等算子对区间直觉模糊信息进行集结,可以充分考虑不同利益相关者在评价过程中的话语权,有效规避评价主体因主观偏好所引起的偏差。最后通过算例分析表明该方法的有效性和合理性。     

Multivariate normality via conditional specification

If X is a k-dimensional random vector, we denote by X_(i) the vector X with coordinate i deleted and by X_(i,j) the vector X with coordinates i and j deleted. If for each i the conditional distribution of X_i given X_(i) = x_(i) is univariate normal for each x_(i) ^K−1 and if for each i, j the conditional distribution of X_i given X_(i,j) = x_(i,j) is univariate normal for each x_(i,j) ^k−2 then it is shown that X has a classical k-variate normal distribution.     

A two-sided estimate in the Hsu-Robbins-Erdös law of large numbers

Let X₁, X₂, … be independent identically distributed random variables. Then, Hsu and Robbins (1947) together with Erdös (1949, 1950) have proved that

,

if and only if E[X²₁] < ∞ and E[X₁] = 0. We prove that there are absolute constants C₁, C₂ (0, ∞) such that if X₁, X₂, … are independent identically distributed mean zero random variables, then

c₁λ⁻² E[X₁²·1_{|X1|λ}]S(λ)C₂λ⁻² E[X₁²·1_{|X1|λ}]

,

for every λ > 0.     

Efficient robust estimation of parameter in the random censorship model

For an open set Θ of ^k, let \s{P_θ: θ Θ\s} be a parametric family of probabilities modeling the distribution of i.i.d. random variables X₁,…, X_n. Suppose X_i's are subject to right censoring and one is only able to observe the pairs (min(X_i, Y_i), [X_i Y_i]), i = 1,…, n, where [A] denotes the indicator function of the event A, Y₁,…, Y_n are independent of X₁,…, X_n and i.i.d. with unknown distribution Q₀. This paper investigates estimation of the value θ that gives a fitted member of the parametric family when the distributions of X₁ and Y₁ are subject to contamination. The constructed estimators are adaptive under the semi-parametric model and robust against small contaminations: they achieve a lower bound for the local asymptotic minimax risk over Hellinger neighborhoods, in the Hájel—Le Cam sense. The work relies on Beran (1981). The construction employs some results on product-limit estimators.     

Additive Maps Preserving Nilpotent Perturbation of Scalars

Let X be a Banach space over F(= R or C) with dimension greater than 2. Let N(X) be the set of all nilpotent operators and B_0(X) the set spanned by N(X). We give a structure result to the additive maps on FI + B_0(X) that preserve rank-1 perturbation of scalars in both directions. Based on it, a characterization of surjective additive maps on FI + B_0(X) that preserve nilpotent perturbation of scalars in both directions are obtained. Such a map Φ has the form either Φ(T) = cAT A~(-1)+ φ(T)I for all T ∈ FI + B_0(X) or Φ(T) = cAT*A~(-1)+ φ(T)I for all T ∈ FI + B_0(X), where c is a nonzero scalar,A is a τ-linear bijective transformation for some automorphism τ of F and φ is an additive functional.In addition, if dim X = ∞, then A is in fact a linear or conjugate linear invertible bounded operator.     

Ranks of Solutions of the Matrix Equation AXB = C

The purpose of this article is to solve two problems related to solutions of a consistent complex matrix equation AXB = C : (I) the maximal and minimal ranks of solution to AXB = C , and (II) the maximal and minimal ranks of two real matrices X₀ and X₁ in solution X = X₀ + iX₁ to AXB = C . As applications, the maximal and minimal ranks of two real matrices C and D in generalized inverse (A + iB)^- = C + iD of a complex matrix A + iB are also examined.     

Invariant record processes and applications to best choice modelling

Let X₁, X₂,…be identically distributed random variables from an unknown continuous distribution. Further let I_r(1), I_r(2),…be a sequence of indicator functions defined on X₁, X₂,…by I_r(k) = 0 if k < r, I_r(k) = 1 if X_k is a r-record AND = 0 otherwise. Suppose that we observe X₁, X₂,… at times T₁ < T₂ <… where the T_k's are realisations of some regular counting process (N(τ)) defined on the positive half-line. Having observed [0, τ], say, the problem is to predict the future behaviour of the counting processes (R_r(τ, s))_sτ = # r-records in [τ, s]. More specifically the objective of this paper is to show that these processes can be (inhomogeneous) Poisson processes even if (N(τ))_τ0 has dependent increments.

The strong link between optimal selection and optimal stopping of record sequences or record processes, perhaps not fully recognized so far, is pointed out in this paper. It is shown to lead to a unification of the treatment of problems which, at first sight, are rather different. Moreover the stopping of record processes in continuous time can lead to rigorous and elegant solutions in cases where dynamic programming is bound to fail. Several examples will be given to facilitate a comparison with other methods.     

First passage time for some stationary processes

For a 1-dependent stationary sequence {X_n} we first show that if u satisfies p₁=p₁(u)=P(X₁>u)0.025 and n>3 is such that 88np₁³1, then

P{max(X₁,…,X_n)u}=ν·μⁿ+O{p₁³(88n(1+124np₁³)+561)}, n>3,

where

ν=1−p₂+2p₃−3p₄+p₁²+6p₂²−6p₁p₂,μ=(1+p₁−p₂+p₃−p₄+2p₁²+3p₂²−5p₁p₂)⁻¹

with

p_k=p_k(u)=P{min(X₁,…,X_k)>u}, k1

and

|O(x)||x|.

From this result we deduce, for a stationary T-dependent process with a.s. continuous path {Y_s}, a similar, in terms of P{max_0skTY_s<u}, k=1,2 formula for P{max_0stY_su}, t>3T and apply this formula to the process Y_s=W(s+1)−W(s), s0, where {W(s)} is the Wiener process. We then obtain numerical estimations of the above probabilities.     

On a property specific to the tent map

Let a set {X_λ; λ  Λ} of subspaces of a topological space X be a cover of X. Mathematical conditions are proposed for each subspace X_λ to define a map g_Xλ:X_λ→X which has the following property specific to the tent map known in the baker’s transformation. Namely, for any infinite sequence ω₀, ω₁, ω₂, … of X_λ, λ  Λ, we can find an initial point x₀  ω₀ such that g_ω0(x₀)ω₁,g_ω1(g_ω0(x₀))ω₂,…. The conditions are successfully applied to a closed cover of a weak self-similar set.     

Estimating the spectral measure of an extreme value distribution

Let (X₁, Y₁), (X₂, Y₂),…, (X_n, Y_n) be a random sample from a bivariate distribution function F which is in the domain of attraction of a bivariate extreme value distribution function G. This G is characterized by the extreme value indices and its spectral measure or angular measure. The extreme value indices determine both the marginals and the spectral measure determines the dependence structure. In this paper, we construct an empirical measure, based on the sample, which is a consistent estimator of the spectral measure. We also show for positive extreme value indices the asymptotic normality of the estimator under a suitable 2nd order strengthening of the bivariate domain of attraction condition.     

A characterization of multivariate normal distribution and its application

Let X₁, X₂, …, X_n be i.i.d. d-dimensional random vectors with a continuous density. Let and . In this paper we find that the distribution of Z_k (or Y_k) can be used for characterizing multivariate normal distribution. This characterization can be employed for testing multivariate normality in terms of the so-called transformation method.