基于跳-扩散模型的股票挂钩型理财产品的资产定价

本文在假定股票价格服从跳-扩散过程的基础上,研究两种常见的股票挂钩型理财产品的资产定价问题.首先,基于异常值检测方法对跳-扩散模型的参数进行估计,基于矩估计方法对几何布朗运动模型的参数进行估计,并对参数估计的有效性进行评估;然后,依据参数估计的结果对保本型理财产品和阈值型理财产品分别定价,并分析跳对产品价格的影响.对于本文涉及的保本型理财产品和阈值型理财产品,数值模拟发现:含跳过程的模型更能描述原始股价的波动情况,且股票价格服从跳-扩散模型时,两种理财产品的价格均高于股票价格服从几何布朗运动时的价格,从而说明跳过程所描述的这类事件会影响股票价格,并对理财产品的价格产生显著影响.因此,本文对含跳过程股票挂钩型理财产品的定价研究具有一定的现实意义.     

变系数ARCH-M模型的ARCH效应检验

本文考虑变系数ARCH—M模型,构造了非参数部分和参数部分的截面似然估计。基于估计的渐近性质,构造了Wald检验统计量来检验模型是否具有条件异方差性。数值模拟结果表明,所构造的估计和Wald统计量具有良好的有限样本性质。     

序约束下ARCH(0,2)模型参数估计与检验

本文研究了平稳ARCH（0，2）模型未知参数α的极大似然估计及有序约束时α的极大似然估计的渐近性质，给出了参数序关系（α1≥α2）的检验方法，并得出了似然比检验统计量的渐近分布。用二次规划的算法，给出求各种情况下参数α的极大似然估计的数值算法。     

双截尾Tobit模型中的随机加权逼近方法

本文研究双截尾删失回归模型中参数的随机加权估计(RWE),获得了RWE的统计渐近性质,如相合性和渐近分布.本文证明了RWE在给定样本下的条件渐近分布与参数的最小绝对偏差(LAD)估计的渐近分布是一样的,则可以利用RWE的条件分布去逼近回归参数的LAD估计的分布,从而避免冗余参数的估计,如误差项的密度函数.另外,本文也提出了一个M检验统计量和随机加权M检验统计量(RWM)来检验参数的线性假设问题,建立了该检验的统计性质.数值模拟和实际数据分析结果表明所提方法是可行的.     

部分线性变系数模型的Profile Lagrange乘子检验

对于部分线性变系数模型附有约束条件时的估计与检验问题,基于Profile最小二乘方法给出了参数部分以及非参数部分的约束估计并研究了它们的渐近性质,并针对约束条件构造了Profile Lagrange乘子检验统计量,证明了该统计量在原假设下的渐近分布为χ2分布,从而将Lagrange乘子检验方法推广到了半参数模型上.     

基于M估计的纵向数据线性混合模型中方差的齐性检验

本文对纵向数据的线性混合模型,用Fisher得分法得到了参数的M估计(稳健估计),给出了其渐近性质,研究了M估计下异方差的Score检验问题,并对检验统计量的功效进行了模拟,最后通过葡萄糖数据的实例说明了本文方法的有效性。     

一类半参数GARCH-M模型的统计检验

半参数GARCH-M模型能够对资本市场的相对风险厌恶进行度量,本文利用经验似然方法对风险厌恶是否受到外生变量的影响进行检验。论文首先讨论了模型的参数估计及其渐近性质,其次利用估计方程构造检验统计量并证明其渐近服从卡方分布,最后进行了数值模拟。结果表明估计精度较高,检验统计量对备择假设比较敏感。     

基于M估计的线性混合效应模型中方差的齐性检验

本文对纵向数据的线性混合模型,用Fisher得分法得到了参数的M估计(稳健估计),给出了其渐近性质,研究了M估计下异方差的Score检验问题,并对检验统计量的功效进行了模拟,最后通过葡萄糖数据的实例说明了本文方法的有效性.     

部分函数型线性空间自回归模型的假设检验

本文提出了部分函数型线性空间自回归模型的空间效应以及参数效应的假设检验问题.首先利用函数型主成分分析方法估计斜率函数,利用广义矩估计方法估计参数.然后利用得到的相合估计,在原假设和备择假设下,构造了基于残差平方和的检验统计量,同时给出了此检验统计量的渐近性质.模拟结果表明在有限样本下,检验统计量具有良好表现.最后将部分函数型线性空间自回归模型的检验应用到一个关于经济增长的数据案例中,说明所提出的检验统计量的应用表现.     

一类函系数ARCH-M模型的经验似然检验

本文利用经验似然方法对一类函系数ARCH-M模型的非参数分量进行检验。首先讨论了该模型的参数估计及其渐进性质,其次利用估计方程构造了经验似然比统计量来检验模型的非参数分量是否为一已知函数。数值模拟结果表明论文所提出的检验统计量对备择假设是相当灵敏的。     

Nonlinear Least Squares Estimation of Log-ACD Models

This paper studies a nonlinear least squares estimation method for the logarithmic autoregressive conditional duration (Log-ACD) model. We establish the strong consistency and asymptotic normality for our estimator under weak moment conditions suitable for applications involving heavy-tailed distributions. We also discuss inference for the Log-ACD model and Log-ACD models with exogenous variables. Our results can be easily translated to study Log-GARCH models. Both simulation study and real data analysis are conducted to show the usefulness of our results.     

一类HIV/AIDS流行病模型

结合某市的艾滋病现状给出了相应的传染病动力学模型,研究了其平衡点的稳定性,讨论了流行病的阈值,并对不同的说服率、不同的因病死亡率、不同的传染率分别进行了数值模拟,对该市艾滋病的预防和控制给出了理论上的指导和建议.     

Spreading of epidemics on scale-free networks with nonlinear infectivity

In this paper, we study the spreading of epidemics on scale-free networks with infectivity which is nonlinear in the connectivity of nodes. We will show that the nonlinear infectivity is more appropriate than constant or linear ones, and give the epidemic threshold of the SIS model on a scale-free network with nonlinear infectivity. In addition, we compare the effects of nonlinear infectivity on the epidemic threshold with two other cases on infinite and finite scale-free networks, and find some new results, such as: with unit recovery rate and nonlinear irrational infectivity, the epidemic threshold is always positive; and the epidemic threshold can increase with network size on finite networks, contrary to the findings in all previous work.     

单种群阶段结构的生育脉冲模型

本文研究单种群阶段结构生育脉冲的数学模型,通过研究其频闪映射所确定的离散动力系统,我们获得了生育脉冲的系统存在周期解及其稳定的阈值,阐述了阈值的生物意义.     

Bifurcation and chaos in a Monod type food chain chemostat with pulsed input and washout

In this paper, we introduce and study a model of a Monod type food chain chemostat with pulsed input and washout. We investigate the subsystem with substrate and prey and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, prey and predator. Simple cycles may give way to chaos in a cascade of period-doubling bifurcations. Furthermore, by comparing bifurcation diagrams with different bifurcation parameters, we can see that the impulsive system shows two kinds of bifurcations, whose are period-doubling and period-halving.     

Modelling Dependence Uncertainty in the Extremes of Markov Chains

General theory on the extremes of stationary processes leads only to a limited representation for extreme-state behaviour, usually summarised by the extremal index. In practice this means that other quantities such as the duration of extreme episodes or aggregate of threshold exceedances within a cluster require stronger model assumptions. In this paper we propose a model based on a Markov assumption for the underlying process, with high-level transitions determined by an asymptotically motivated distribution. This idea is not new: Smith et al. (1997) first developed the statistical basis for such a procedure, which was subsequently extended by Bortot and Tawn (1998) to better handle the case of weak extremal temporal dependence for which the extremal index is unity. We adopt similar procedures to each of these earlier works, but suggest a different model for the Markov transitions. The model we use was developed by Coles and Pauli (2002) to enable a Bayesian inference of multivariate extremes that provides a posterior distribution on the status of asymptotic independence. By adopting this model in the Markov framework, we show here that the model has all the flexibility of the model developed by Bortot and Tawn (1998), but with the additional advantage of providing a posterior probability on the extremal index and inferences that take full account of the uncertainty in the extremal index. We demonstrate the methodology on both simulated data and a time series of daily rainfall that exhibit weak temporal dependence at extreme levels.     

Enumeration of labelled threshold graphs and a theorem of frobenius involving eulerian polynomials

We enumerate labelled threshold graphs by the number of vertices, the number of isolated vertices, and the number of distinct vertex-degrees and we give the exact asymptotics for the number of labelled threshold graphs withn vertices. We obtain the appropriate generating function and point out a combinatorial interpretation relating its coefficients to the Stirling numbers of the second kind. We use these results to derive a new proof of a theorem of Frobenius expressing the Eulerian polynomials in terms of the Stirling numbers.     

多次分组会议安排的最佳混合方案

本文在仔细分析问题条件和要求的基础上,运用了运筹学、图论、矩阵理论和置换等方面的知识和技巧,建立了一个布尔规划模型。     

Log canonical thresholds of del Pezzo surfaces in characteristic p

The global log canonical threshold of each non-singular complex del Pezzo surface was computed by Cheltsov. The proof used Kollár–Shokurov’s connectedness principle and other results relying on vanishing theorems of Kodaira type, not known to be true in finite characteristic. We compute the global log canonical threshold of non-singular del Pezzo surfaces over an algebraically closed field. We give algebraic proofs of results previously known only in characteristic 0. Instead of using of the connectedness principle we introduce a new technique based on a classification of curves of low degree. As an application we conclude that non-singular del Pezzo surfaces in finite characteristic of degree lower or equal than 4 are K-semistable.