数值求解不可压Navier-Stokes方程的隐式算法

本文提出了一个求解二维不可压Navier-Stokes方程的隐式算法。这种方法隐式联立地处理了控制方程,和一般的迭代算法相比它具有更好的稳定性和收敛性。二维Poissuill流动的数值解和分析解是非常一致的,S形流道内分离流的计算结果和实验结果相比也是令人满意的。     

线性代数教学实践中的体会

结合线性代数课程本身的特点和学生实际情况,通过对线性代数课程的教学实践,提出了线性代数抽象概念讲解要与具体实例相结合,激发学生的学习兴趣,提高学生分析、归纳、总结和演绎的基本素质,改进教学方法和手段等措施来提高课程的教学质量。     

A new higher-order weak approximation scheme for stochastic differential equations and the Runge–Kutta method

The authors report on the construction of a new algorithm for the weak approximation of stochastic differential equations. In this algorithm, an ODE-valued random variable whose average approximates the solution of the given stochastic differential equation is constructed by using the notion of free Lie algebras. It is proved that the classical Runge–Kutta method for ODEs is directly applicable to the ODE drawn from the random variable. In a numerical experiment, this is applied to the problem of pricing Asian options under the Heston stochastic volatility model. Compared with some other methods, this algorithm is significantly faster. This research was partly supported by the Ministry of Education, Science, Sports and Culture, Grant-in-Aid for Scientific Research (C), 15540110, 2003 and 18540113, 2006, the 21st century COE program at Graduate School of Mathematical Sciences, the University of Tokyo, and JSPS Core-to-Core Program 18005.     

Bartlett adjustments for systems of linear equations with linear restrictions

Simple matrix formulae are derived for calculating a Bartlett adjustment to the likelihood ratio test statistic for testing linear parameter restrictions in a system of linear equations. For the special case of column and/or row restrictions on the matrix of coefficients the adjustment is a simple function of matrix dimensions being invariant to sample observations and the error covariance matrix. An example of testing for homogeneity and symmetry in a demand system is given.     

The geography of trade in goods and asset holdings

Gravity models have been widely used to describe bilateral trade in goods. Portes and Rey [Portes, R., Rey, H., 2005. The Determinants of Cross-Border Equity Flows. Journal of International Economics, 65(2), 269-296.] applied this framework to cross-border equity flows and found that distance, which proxies information asymmetries, is a surprisingly very large barrier to cross-border asset trade. We adopt a different point of view and explore the complementarity between bilateral trade in goods and bilateral asset holdings in a simultaneous gravity equations framework. Providing different instruments for both endogenous variables, we show that a 10% increase in bilateral trade raises bilateral asset holdings by 6% to 7%. The reverse causality is also significant, albeit smaller. Controlling for trade, the impact of distance on asset holdings is drastically reduced.     

Poisson Regression for Clustered Data

We compare five methods for parameter estimation of a Poisson regression model for clustered data: (1) ordinary (naive) Poisson regression (OP), which ignores intracluster correlation, (2) Poisson regression with fixed cluster‐specific intercepts (FI), (3) a generalized estimating equations (GEE) approach with an equi‐correlation matrix, (4) an exact generalized estimating equations (EGEE) approach with an exact covariance matrix, and (5) maximum likelihood (ML). Special attention is given to the simplest case of the Poisson regression with a cluster‐specific intercept random when the asymptotic covariance matrix is obtained in closed form. We prove that methods 1–5, except GEE, produce the same estimates of slope coefficients for balanced data (an equal number of observations in each cluster and the same vectors of covariates). All five methods lead to consistent estimates of slopes but have different efficiency for unbalanced data design. It is shown that the FI approach can be derived as a limiting case of maximum likelihood when the cluster variance increases to infinity. Exact asymptotic covariance matrices are derived for each method. In terms of asymptotic efficiency, the methods split into two groups: OP & GEE and EGEE & FI & ML. Thus, contrary to the existing practice, there is no advantage in using GEE because it is substantially outperformed by EGEE and FI. In particular, EGEE does not require integration and is easy to compute with the asymptotic variances of the slope estimates close to those of the ML.     

非线性延迟系统Runge-Kutta方法的稳定性探讨

针对时间依赖型的非线性多变延迟系统,采用变步长的Runge-Kutta方法求解,证明了匹配一定插值方法的代数稳定的Runge-Kutta方法是VR稳定的。     

贸易摩擦对中国钢铁产品出口影响的实证研究

随着中国钢铁产业快速的发展和世界经济环境的变化,涉华钢铁产品贸易摩擦日趋激烈。文章分析了中国钢铁产品出口贸易摩擦的概况,运用理论分析与实证分析相结合的方法,详细分析贸易摩擦对中国钢铁产品出口规模、出口市场结构以及国际竞争力的影响,对贸易摩擦的影响进行了总结:负面影响主要是出口规模的萎缩、限制相关企业的发展和提高出口贸易的成本,正面影响主要是促进贸易地理方向的多元化、产生优胜劣汰效应和促进技术创新。     

Can good marketing carry a bad product? Evidence from the motion picture industry

We examine the relative roles of marketing actions and product quality in determining commercial success. Using the motion picture context, in which product quality is difficult for consumers to anticipate and information on product success is available for different points in time, we model the effects of studio actions and movie quality on a movie’s sales during different phases of its theatrical run. For a sample of 331 recent motion pictures, structural equation modeling demonstrates that studio actions primarily influence early box office results, whereas movie quality influences both short- and long-term theatrical outcomes. The core results are robust across moderating conditions. We identify two data segments with follow-up latent class regressions and explore the degree of studio actions needed to “save” movies of varying quality. We finally offer some implications for research and management.     

PROPERTIES OF OPTION PRICES IN MODELS WITH JUMPS

We study convexity and monotonicity properties of option prices in a model with jumps using the fact that these prices satisfy certain parabolic integro–differential equations. Conditions are provided under which preservation of convexity holds, i.e., under which the value, calculated under a chosen martingale measure, of an option with a convex contract function is convex as a function of the underlying stock price. The preservation of convexity is then used to derive monotonicity properties of the option value with respect to the different parameters of the model, such as the volatility, the jump size, and the jump intensity.