套代数的直和算子集及可逆算子

本文研究了套代数的一个直和算子集X_N^φ,得到套代数的直和分解:τ(N)=D_N⊕X_N^φ,同时讨论了套代数中可逆算子的分布,得出套代数的对角D_N关于可逆算子是封闭的。特别地,当套为可数套时,套代数关于可逆性算子封闭的充要条件为φ(T)可逆。     

基于Spearman ρ的时变Copula模型的模拟及应用

本文从Spearmanρ入手,利用Spearmanρ在非线性单调变换的情况下保持不变的特点,以及与条件期望预测机制存在的非线性的关系,提出建立时变Copula的模型的新方法;通过建立时变FGM-Copula模型的实例分析表明,这种构建Copula模型的方法较好捕捉了相依机制的时变性,预测了随机变量的趋势,具有一定的优越性。     

On the study of a rational expectation model with lagged endogenous variables

A rational expectation model with lagged endogenous variables is used to describe how the current price level is influenced by the expectation and historic price level. The time domain of the rational expectation model is extended to a complex discrete time domain which is a collection of points along the real number line. The rational expectation model with lagged endogenous variables is solved in multi-dimensional cases where the agents possess multiple assets, and the current price of each asset is related to the expected price and historical prices. An example about price determination process of storable commodities is given to illustrate the advantages of the rational expectation model on isolate time domain.     

RELATIVE ENTROPY AND LARGE DEVIATIONS UNDER SUBLINEAR EXPECTATIONS

We give a definition of relative entropy with respect to a sublinear expectation and establish large deviation principle for the empirical measures for independent random variables under the sublinear expectation.     

基于社会敏感问题的问卷调查方案设计与分析

利用概率论与数理统计方法,以对酒后驾车现象为例,就社会敏感问题的问卷调查方案设计,建立数学模型,并对模型结果进行分析.     

Multivariate Tweedie distributions and some related capital-at-risk analyses

We study a multivariate extension of the univariate exponential dispersion Tweedie family of distributions. The class, referred to as the multivariate Tweedie family (MTwF), on the one hand includes multivariate Poisson, gamma, inverse Gaussian, stable and compound Poisson distributions and on the other hand introduces a high variety of new dependent probabilistic models unstudied so far. We investigate various properties of MTwF and discuss its possible applications to financial risk management.     

On the Tail Mean-Variance optimal portfolio selection

In the present paper we propose the Tail Mean-Variance (TMV) approach, based on Tail Condition Expectation (TCE) (or Expected Short Fall) and the recently introduced Tail Variance (TV) as a measure for the optimal portfolio selection. We show that, when the underlying distribution is multivariate normal, the TMV model reduces to a more complicated functional than the quadratic and represents a combination of linear, square root of quadratic and quadratic functionals. We show, however, that under general linear constraints, the solution of the optimization problem still exists and in the case where short selling is possible we provide an analytical closed form solution, which looks more “robust” than the classical MV solution. The results are extended to more general multivariate elliptical distributions of risks.