非线性模型中VaR估测的正态性改进

VaR风险测度技术已经被学界和业界广泛使用,但其局限性也是显而易见的,国内外学者对其进行了一系列的改进.由线性模型扩展为非线性模型以及由正态假定转换到非正态性均源于风险测度的精确化.探讨依数据特征改进和扩展VaR估测方法,使用Johnson转换方法与Cornish-Fisher扩展方法这两种正态性改进方法改善VaR估值,一方面利用正态假定成熟理论结果简化VaR估测方法的推演,另一方面从实证分析角度论证了正态性改进方法在VaR估测中的准确性与有效性.     

非线性边值条件非线性方程的奇摄动问题

研究了三阶非线性边值条件的非线性方程奇摄动问题,先用合成展开法对形式近似解进行构造,再利用相关微分不等式理论给出所得解的存在性及一致有效性的证明.     

一类具有无穷边界值的二次奇摄动边值问题

研究一类具有无穷边界值的二次奇摄动Robin边值问题解的存在性与解的渐进行为,重点关注边界值的奇异程度对解的边界层行为的影响;同时将所得的结果与Chang及Howes的结果(带正常边界值)进行比较.研究表明:(1)当边界值大小为O(1/)时,得到的边界层大小为O( ln ),这比Chang及Howes带正常边界值的情形提高了O(ln )量级;(2)增大边界值的奇性至O(1/ r),这里r >1,边界层大小的量级不变,依然为O( ln );(3)若要使得边界层大小为O(1),则边界值的大小需为O(e?1/).最后给出一个算例验证得到的结果.     

基于强混合数据的半参数平滑转换回归模型

本文基于严平稳强混合数据和带确定性趋势的强混合数据序列,推广了文献[20]中提出的半参数平滑转换回归模型。对含于平滑转换函数中的未知光滑有界函数应用级数估计方法,并基于非线性最小二乘估计和级数估计理论证明了模型参数估计量的相合性和渐近正态性等大样本性质,简要讨论了其协方差矩阵的估计以及假设检验问题。最后,应用该模型重新研究了我国年度通货膨胀率的平滑转换结构。     

非时齐扩散模型中时变参数的局部线性估计

本文主要研究非时齐扩散模型中时变的漂移参数和扩散参数的局部线性估计。基于非时齐扩散模型的离散观测样本,首先得到了漂移参数的局部线性估计及其标准误差。然后,考虑到扩散参数的非负性,本文利用局部对数线性拟合的方法得到了扩散参数的核函数加权估计,并讨论了扩散项估计的渐近偏差、渐近方差和渐近正态性。最后,通过模拟研究表明所得局部估计有很好的拟合效果。     

Asymptotic Stability and Boundedness of Stochastic Differential Equations with Respect to Semimartingales

In this paper, we shall use multiple Lyapunov functions to establish some sufficient criteria for locating the limit sets of solutions of stochastic differential equations with respect to semimartingales. From them follow many useful results on stochastic asymptotic stability and boundedness, including some classical results as special cases. In particular, our new asymptotic stability criteria do not require the diffusion operator associated with the underlying stochastic differential equation be negative definite, while most of the existing results do require this negative definite property essentially.     

Stationary Solution of a Stochastic Nosocomial Epidemic Model in Hospital Intensive Care Units

In this article, the authors consider a stochastic differential equation model of an antibiotic resistant infection epidemic in a hospital intensive care unit. A set of criteria on the existence of the stationary solution and its dynamical behavior are obtained. Numerical simulations are also performed to verify the results.     

Global stability and bifurcations of perturbed Gumowski–Mira difference equation

A generalized convergence theorem for higher order difference equations is established by quasi-Lyapunov function method. From this stability result we deduce the existence of global asymptotically stable fixed point and attractive two-periodic solution of the perturbed Gumowski–Mira difference equation. We also study global bifurcations of this system as the parameters vary. For instance we show that as the recombination coefficient moves through a critical curve, a fixed point loses its asymptotic stability and an attractive cycle of period 2 emerges near the fixed point due to a period-doubling bifurcation. The associated existence regions are also located.     

Asymptotic theory for delay differene equations

Using the new notion of block dichotomy we investigate the asymptotic behavior of nonlinear delay difference equations. Our results produce a discrete analogue of Levinson-type theorems.     

Coexisting holes and electrons in high-T C materials: implications from normal state transport

Normal state resistivity and Hall effect are shown to be successfully modeled by a two-band model of holes and electrons that is applied self-consistently to (i) dc transport data reported for eight bulk-crystal and six oriented-film specimens of YBa₂Cu₃O_7?δ, and (ii) far-infrared Hall angle data reported for YBa₂Cu₃O_7?δ and Bi₂Sr₂CaCu₂O_8+δ. The electron band exhibits extremely strong scattering; the extrapolated dc residual resistivity of the electronic component is shown to be consistent with the previously observed excess thermal conductivity and excess electrodynamic conductivity at low temperature. Two-band hole–electron analysis of Hall angle data suggests that the electrons possess the greater effective mass.