Brownian–Laplace Motion and Its Use in Financial Modelling

Brownian-Laplace motion is a Lévy process which has both continuous (Brownian) and discontinuous (Laplace motion) components. The increments of the process follow a generalized normal Laplace (GNL) distribution which exhibits positive kurtosis and can be either symmetrical or exhibit skewness. The degree of kurtosis in the increments increases as the time between observations decreases. This and other properties render Brownian-Laplace motion a good candidate model for the motion of logarithmic stock prices. An option pricing formula for European call options is derived and it is used to calculate numerically the value of such an option both using nominal parameter values (to explore its dependence upon them) and those obtained as estimates from real stock price data.     

How Often Likelihood Ratios are Misleading in Sequential Trials

How often would investigators be misled if they took advantage of the likelihood principle and used likelihood ratios—which need not be adjusted for multiple looks at the data—to frequently examine accumulating data? The answer, perhaps surprisingly, is not often. As expected, the probability of observing misleading evidence does increase with each additional examination. However, the amount by which this probability increases converges to zero as the sample size grows. As a result, the probability of observing misleading evidence remains bounded—and therefore controllable—even with an infinite number of looks at the data. Here we use boundary crossing results to detail how often misleading likelihood ratios arise in sequential designs. We find that the probability of observing a misleading likelihood ratio is often much less than its universal bound. Additionally, we find that in the presence of fixed-dimensional nuisance parameters, profile likelihoods are to be preferred over estimated likelihoods which result from replacing the nuisance parameters by their global maximum likelihood estimates.     

Repeated Confidence Intervals Under Fractional Brownian Motion in Long-Term Clinical Trials

Repeated confidence interval (RCI) is an important tool for design and monitoring of group sequential trials according to which we do not need to stop the trial with planned statistical stopping rules. In this article, we derive RCIs when data from each stage of the trial are not independent thus it is no longer a Brownian motion (BM) process. Under this assumption, a larger class of stochastic processes fractional Brownian motion (FBM) is considered. Comparisons of RCI width and sample size requirement are made to those under Brownian motion for different analysis times, Type I error rates and number of interim analysis. Power family spending functions including Pocock, O'Brien-Fleming design types are considered for these simulations. Interim data from BHAT and oncology trials is used to illustrate how to derive RCIs under FBM for efficacy and futility monitoring.     

Testing for the Equality of Two Nonparametric Regression Curves with Long Memory Errors

This article discusses the problem of testing the equality of two nonparametric regression functions against two-sided alternatives for uniform design on [0,1] with long memory moving average errors. The standard deviations and the long memory parameters are possibly different for the two errors. The article adapts the partial sum process idea used in the independent observations settings to construct the tests and derives their asymptotic null distributions. The article also shows that these tests are consistent for general alternatives and obtains their limiting distributions under a sequence of local alternatives. Since the limiting null distributions of these tests are unknown, we first conducted a Monte Carlo simulation study to obtain a few selected critical values of the proposed tests. Then based on these critical values, another Monte Carlo simulation is conducted to study the finite sample level and power behavior of these tests at some alternatives. The article also contains a simulation study that assesses the effect of estimating the nonparametric regression function on an estimate of the long memory parameter of the errors. It is observed that the estimate based on direct observations is generally preferable over the one based on the estimated nonparametric residuals.     

基于免疫原理的控制器参数整定方法

基于免疫原理,建立了一个基于免疫机制进行控制器参数整定的数学模型。给出了参数整定问题中抗原、抗体和亲和力的定义,对基于免疫原理的控制器参数整定过程进行了详细的描述。最后以PID的参数整定为例,控制一个高阶系统,大延迟系统和非最小相位系统。并与Z-N,MOMI等算法的整定结果进行了对比实验,结果表明该方法对控制器的参数整定是有效的。     

分数布朗运动下B-S权证定价模型的修正

分析证券市场的有效性,指出其线性范式与现实市场状况并不符合。传统的金融学认为证券收益率服从对数正态分布,而大量的实证表明收益率分布与正态分布相比有＂尖峰胖尾＂特征,具有分形结构。在此基础上剖析了传统B-S权证定价模型的不足,结合分形市场中的分数布朗运动,提出了基于分形理论的B-S股本权证定价模型,考虑了股本稀释效应。由于股本权证定价模型需要已知企业股权价值及其波动率,但企业价值是权证价格的函数。基于此,运用数值方法以股票价格和波动率来估计企业价值波动率,并给出了在实际运用中的案例。     

改进运动规律凸轮基圆半径的确定

本文针对凸轮机构推杆作改进梯形加速度、改进正弦加速度和３－４－５次多项式运动规律的情况，研究对心式盘形凸轮机构凸轮基圆半径的确定方法，并利用数值计算方法绘制了基圆半径系数β（ｒ＿０／ｈ）的线图．本文是对已有的用于四种基本运动规律确定基圆半径的诺模图￣［３］和补充诺模图［６］的进一步的发展．     

牛顿运动定律对大学生心理健康教育的启示

具有浓重哲学内蕴的牛顿力学三大运动定律对当前大学生心理健康教育具有一定启示,可借鉴牛顿第一运动定律、牛顿第二运动定律（加速度定律）和牛顿第三运动定律（作用力与反作用力定律）,分别从心理健康教育中重要的三个环节,即“立志”、“修身”和“崇尚仁爱”出发,引导学生建立自强不息、厚德栽物的完善人格及心理品质。同时,心理教育中三个环节之间相辅相成、和谐统一的关系也印证了牛顿三大运动定律之间的整体性和统一性。将心理健康教育与其他学科进行交叉融合,有利于促进大学生心理健康教育工作的创新性、文化性和个性化发展。     

英汉运动动词的图式结构比较简

对运动句式的分析表明“始源-路径-目标”图式可表达移动者的动作。英、汉两种语言都可以用动词和介词两种语法形式表示空间关系的图式信息,即表明移动者位置的改变,同时还可以表达其他信息。     

论李长之的文学观

李长之是现代文学史上著名的批评家。他的文学观是东方和西方、传统和现代的结合。他在强调文学是纯粹直观的情感活动的同时,并不否定文学的客观的社会功利价值;认为文学和人生是有联系的,但并不追求"为人生";在文学与时代的关系上,主张抓住艺术的时代,追求艺术的真实;对于作家,李长之认为应充分发挥作家作为创作主体的个性,形成自己的风格。这些文学观念是其文学批评的理论前提。