Modeling Default Dependence with the Mixture of Calendar Time and Business Time

Evaluating default correlation between securities in a portfolio is very important for credit derivatives pricing and risk management. Under the framework of the structural model proposed by Black and Cox, we assume that the asset values of companies are driven by Brownian motions in the worlds of the calendar time and the business time; they then could evolve continuously or by leap. We build the dynamic default correlations using the time-varying correlated Brownian motions in these processes. The sensitivity of default correlations to the key parameters is explored in the paper by numerical examples, and we apply the model to risk management as well. Because default times are unpredictable in the proposed model, the defaults might occur suddenly. Independent defaults and complete correlated defaults can be described in the model as well.     

两类包含子图K_(1,m,n)和W_n的优美图

用构造的方法给出K1,m,n+Emn+1和Wn+En+1的优美标号,从而证明了K1,m,n+Emn+1和Wn+En+1都是优美图.     

基于剩余寿命的劣化系统最优维修策略

考虑Gamma型劣化可替换系统的最优观测/替换策略问题,给出了基于剩余寿命的观测函数,得到期望单位时间维修费用最小化准则下的最优维修策略.相对于传统的非周期观测策略,该方法只需要一个比例风险系数参数来确定检测时间,从而降低了策略优化过程的复杂性.数值模拟表明在系统长期使用的单位时间维修费用上,基于平均剩余寿命的策略可以得到比一些基于状态的维修策略更优的结果.     

锥度量空间中两个集值映射的公共不动点定理

在度量空间中引入了一种新的广义压缩条件,利用这种条件,在不要求正规锥的前提下,得到了满足广义压缩条件的集值映射的公共不动点的存在性结果.这些结果推广了一些锥度量空间中关于两个集值映射的最常见的公共不动点定理.     

GFC-空间中的参数型KKM定理及其应用

首先证明了GFC-空间的一个特征性质,然后通过引进线性序空间,在非紧的GFC-空间中证明了一个参数型KKM定理.应用参数型KKM定理得到了一些新的非紧的极大极小不等式.     

PA序列生成的线性过程误差权函数估计的Berry-Esseen界

在由PA序列生成的线性过程误差下,讨论了非参数回归函数加权估计的Berry-Esseen界,其Berry-Esseen界可达O(n~(-1/6)).     

一个新的延迟分数阶系统的同步

提出了一个新的延迟分数阶系统.首先,对该延迟系统随延迟项变化的动力学进行了研究;然后,基于分数阶系统的稳定性理论,提出了该系统的同步方案.通过设计合适的同步控制器,实现了系统的同步.数值仿真验证了同步方案的有效性.     

The Classification of States for Markov Chain in Random Environments and m-irreducible

First of all,we introduces the concept of m-irreducible of Markov chain in random environment. Then under the condition of m-irreducible,the relationship of recurrent and positive recurrent between two states is studied. We also give several conditions that can imply a state is recurrent and positive recurrent. And then the period of a state is discussed and we obtained that under the condition of m-irreducible,for any two states in X ,they have the same period.     

EGARCH(1,1)模型对上证指数与成交金额波动性的实证研究

以2010年3月31日-2014年10月28日的上证指数与其成交金额的日数据为样本,对其进行Granger因果检验,采用ARCH族模型,对上证指数与成交金额的波动关系进行了非线性研究,并对EGARCH(1,1)模型运用于成交金额对上证指数日收益率的影响进行了检验和预测.     

Consistency of Chi-Squared Test with Varying Number of Classes

The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.