基于MCMC抽样的金融贝叶斯半参数GARCH模型研究

GARCH模型是研究金融资产收益的重要模型,然而现有参数GARCH模型依然不能有效刻画金融资产收益偏态厚尾特性且存在模型设定风险。本文在非参数分布和GARCH模型基础上,建立半参数GARCH模型以提高模型的有效性;同时在贝叶斯框架内发展有效MCMC抽样解决模型的参数估计难问题,并利用DIC4研究模型比较问题;最后通过模拟研究和实证研究考察MCMC抽样的有效性,检验半参数GARCH模型在刻画金融资产收益特性和风险价值预测方面的实际效果。     

一类金融贝叶斯分位数GARCH模型及其在我国汇率市场中的应用研究

现有GARCH模型依赖于参数条件分布形式假设,依然不能有效刻画金融资产收益偏态厚尾特性,分位数回归能给条件分布提供更加全面的描述.在分位数回归和GJR-GARCH模型基础上建立分位数GJR-GARCH模型,并在贝叶斯框架下对模型进行分析;同时利用中国金融市场数据检验分位数GJR-GARCH模型在风险价值预测方面的实际效果.     

基于参数模型的EVaR风险度量计算方法及实证研究

针对EVaR(Expectile-based Value at Risk)风险度量提出了基于GARCH类和SV波动率模型的EVaR风险度量计算方法,即EVaR计算的参数模型方法.并基于模拟学生t分布时间序列数据,给出EVaR样本外预测的失败率检验方法:Kupiec失败率检验和动态分位数(DQ)检验法.与采用CARE(Conditional Autoregressive Expectile)模型的EVaR计算方法进行了对比研究,结果表明基于GARCH类模型和SV模型相对于基于CARE模型有更优的EVaR预测效果.选取2004年1月5日到2009年12月30日的国内外五个股票市场指数数据,针对日对数收益率进行了EVaR风险度量的实证研究,得出在金融危机期间,基于参数模型的EVaR预测要比基于CARE模型的EVaR预测更接近市场实际风险.     

基于Copula-GJR-Skewt模型的投资组合风险预测研究

针对多元投资组合的风险预测,采用GJR-Skewt模型刻画单资产的厚尾、有偏特征,以及Copula模型刻画多元投资组合的非线性相关结构,用Monte Carlo方法模拟金融资产的随机分布,并结合滚动时间窗法,对投资组合的未来风险进行样本外动态预测.实证结果表明,Copula-GJR-Skewt模型对资产收益的风险预测能取得满意的效果;在VaR预测性能上,以GJR-Skewt模型作为边缘分布函数时,即使存在系统偏差,也能取得最优预测结果;预设残差服从有偏学生分布时,VaR的预测结果优于正态分布;传统的Garch-Guassian模型预测能力最差.     

上海股市波动的预测方式和模型

探讨基于 SV类模型的上海股市波动的预测方式和模型问题 .比较了 SV( stochastic volatility)类模型 (包括基本 SV模型和 ASV模型 )在两种不同方式下的预测效果 ,并将基本 SV类模型的预测效果与 ASV模型 ,以及其他常用模型做了比较 .结果表明 :SV类模型在两种预测方式下的预测效果存在一定的差异 ;基本 SV模型对于上海股市具有较强的预测能力 ;ASV模型的预测效果不理想 .     

SV模型下的期权定价和风险计量

本文利用SV（Stochastic Variance）模型对期权基础资产的收益过程进行统计描述,在同时给出期权定价和市场风险计量之后,又给出定价置信区间和风险置信区间的估计。文中对SV模型作了分析和比较,利用自适应滤波方法对模型的建立和参数的估计给出了简单的方法,最后还对SV模型作了模拟分析并计算了期权定价和风险计量的一个例子。     

SV-M模型下VaR和ES估计的极值方法

本文对随机波动均值内模型(SV-M)应用极值理论(EVT)的方法估计了金融回报的风险价值(VaR)和期望短缺(ES).用SV-M建模异方差金融回报时间序列,刻画了其波动聚类.用蒙特卡罗极大似然方法(MCL)来估计其参数.我们用基于一般帕累托分布(GPD)的EVT拟合SV-M模型的修正分布尾部,刻画了金融时序分布的肥尾特性.因此,本文的极值方法有效地克服了原有方法的缺陷,综合考虑了金融时序的波动聚类及其分布的肥尾特性,给出了合理的VaR和ES估计,对市场风险测度的研究进行了有益的探讨.     

厚尾随机波动率模型的贝叶斯参数估计及实证研究

针对现有时间序列模型难以刻画参数渐变性的问题,对厚尾随机波动(SV)模型的参数估计方法进行了推广,采用基于贝叶斯的MCMC方法,选取2013年5月~2016年6月这一经历多轮震荡的上证指数作为实证分析对象,构造了基于Gibbs抽样的MCMC过程进行仿真分析.结果显示,以卡方分布作为厚尾参数的先验分布能够有效地描述数据波动的厚尾特征,并且能得到较高精度的参数估计结果.结果表明,厚尾SV模型能有效反映出我国股市尖峰厚尾和波动长期记忆性的特征.     

我国股市收益的双长记忆性检验——基于VaR估计的ARFIMA-HYGARcH-skt模型

针对股市收益分布的"尖峰肥尾"特征,引入了偏t分布作为新息分布。基于VaR方法,从风险估计的角度,利用ARFIMA(2,d_1,0)-HYGARCH(1,d_2,1)-skt模型对1996年12月17日至2007年7月5日期间的沪深股市收益进行了实证分析.实证结果显示:沪深股市具有显著的双长记忆特征;上海股市的日收益率和波动率的长记忆性均比深圳股市强;ARFIMA(2,d_1,0)- HYGARCH(1,d_2,1)-skt模型对我国股市收益具有较强的风险估计和预测能力。     

基于广义双曲线分布的我国股票市场VaR风险度量研究

为更好刻画金融资产收益率偏态厚尾特性,提高VaR风险度量精度。本文首先提出利用广义双曲线(GH)分布对收益率数据进行建模型,从分布尾部特性角度对GH分布和其他常用分布进行了比较研究;其次利用EM算法来解决含有Bessel函数的GH分布的参数估计难问题,并运用随机模拟方法计算VaR值;最后讨论GH分布在我国股票市场VaR风险度量中的应用。     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].