Stability and determinacy conditions for mixed-type functional differential equations

This paper analyzes the solution of linear mixed-type functional differential equations with either predetermined or non-predetermined variables. Conditions characterizing the existence and uniqueness of a solution are given and related to the local stability and determinacy properties of the steady state. In particular, it is shown that the relationship between the uniqueness of the solution and the stability of the steady-state is more subtle than the one that holds for ordinary differential equations, and gives rise to new dynamic configurations.     

Estimation of the Option Prime: Microsimulation of Backward Stochastic Differential Equations

A mathematical statistical model is needed to obtain an option prime and create a hedging strategy. With formulas derived from stochastic differential equations, the primes for US Dollar/Chilean Pesos currency options using a prime calculator are obtained. Furthermore, a backward simulation of the option prime trajectory is used with a numerical method created for backward stochastic differential equations. The use of statistics in finance is highly important in order to develop complex products.     

Optimal pollution control with distributed delays

We present a model of optimal stock pollution control with general distributed delays in the stock accumulation dynamics. Using generic functional forms and a distribution structure covering a wide range of distributions, we solve analytically the complex dynamic system that arises from the introduction of these distributed delays. From a theoretical standpoint, our contribution extends the dynamic optimization literature that focused on single discrete delays and develops an original method to address control problems written as mixed type functional differential equations with general kernels. Our results show the qualitative impact of acknowledging these distributed delays on the optimal pollution paths dynamics. We study analytically the properties of the dynamics and we identify the conditions for the occurrence of limit cycles. This theoretical work contributes to the design of efficient environmental policies in the presence of complex delays.     

关于常微分方程教学探索

常微分方程是高等教育的核心基础课程的一部分重要内容,是进一步学习泛函分析,偏微分方程,稳定性理论和控制论等方向的入门学科,具有很强的理论性与应用性的背景,因此,对该部分的教学的教师有责任进行教学设计与探索,以期取得令人满意的教学效果。     

Dynamic Modeling with Structural Equations and Stochastic Differential Equations: Applications with the German Socio-economic Panel

The paper discusses an application of linear dynamic models to multi-wave longitudinal data. Starting from three-wave and four-wave simplex models using standard structural equations, linear dynamic state space models with stochastic differential equations are presented. The main differences between longitudinal structural equations (static view) and stochastic differential equations (dynamic view) are emphasized. Substantively, the models prove the relation, stability and change of two concepts in a period of 10 years: National Identity and Intention to stay in Germany. Data from a sample of migrant workers in Germany included in the German Socio-economic Panel (GSOEP) are used for the analyses. Results and further developments of dynamic models are discussed in the final section.The authors thank Hermann Singer for his comments and discussions on applications of dynamic models.     

On solving bias‐corrected non‐linear estimation equations with an application to the dynamic linear model

In a seminal paper, Mak, Journal of the Royal Statistical Society B, 55, 1993, 945, derived an efficient algorithm for solving non‐linear unbiased estimation equations. In this paper, we show that when Mak's algorithm is applied to biased estimation equations, it results in the estimates that would come from solving a bias‐corrected estimation equation, making it a consistent estimator if regularity conditions hold. In addition, the properties that Mak established for his algorithm also apply in the case of biased estimation equations but for estimates from the bias‐corrected equations. The marginal likelihood estimator is obtained when the approach is applied to both maximum likelihood and least squares estimation of the covariance matrix parameters in the general linear regression model. The new approach results in two new estimators when applied to the profile and marginal likelihood functions for estimating the lagged dependent variable coefficient in the dynamic linear regression model. Monte Carlo simulation results show the new approach leads to a better estimator when applied to the standard profile likelihood. It is therefore recommended for situations in which standard estimators are known to be biased.     

The optimal consumption function in a Brownian model of accumulation Part A: The consumption function as solution of a boundary value problem

We consider a neo-classical model of optimal economic growth with c.r.r.a. utility in which the traditional deterministic trends representing population growth, technological progress, depreciation and impatience are replaced by Brownian motions with drift. When transformed to ‘intensive’ units, this is equivalent to a stochastic model of optimal saving with diminishing returns to capital. For the intensive model, we give sufficient conditions for optimality of a consumption plan (open-loop control) comprising a finite welfare condition, a martingale condition for shadow prices and a transversality condition as t→∞. We then replace these by conditions for optimality of a plan generated by a consumption function (closed-loop control), i.e. a function expressing log-consumption as a time-invariant, deterministic function of log-capital . Making use of the exponential martingale formula we replace the martingale condition by a non-linear, non-autonomous second-order o.d.e. which an optimal consumption function must satisfy; this has the form , where . Economic considerations suggest certain limiting values which and should satisfy as , thus defining a two-point boundary value problem (b.v.p.) — or rather, a family of problems, depending on the values of parameters. We prove two theorems showing that a consumption function which solves the appropriate b.v.p. generates an optimal plan. Proofs that a unique solution of each b.v.p. exists are given in a separate paper (Part B).     

Local determinacy of prices in an overlapping generations model with continuous trading

We characterize the determinacy properties of the intertemporal equilibrium for a continuous-time, pure-exchange, overlapping generations economy with logarithmic preferences. Using recent advances in the theory of functional differential equations, we show that the equilibrium is locally unique and that prices converge to a balanced growth path and are determined.     

三种电离层射线追踪自导引算法比较

通过建立电离层模型和地磁场模型,采用龙格库塔法求解Haselgrove方程,得到相应的射线路径参数,实现了电离层三维射线追踪。针对射线追踪无法进行自导引计算,分别采用牛顿差分自导引算法、基于变分方程的牛顿法以及单纯形法实现了射线追踪的自导引,并给出了详细的算法分析。重点对变分方程及其二阶微分的求解进行了详细推导。最后对以上三种自导引算法进行性能比较,仿真结果表明:基于变分方程的自导引算法优于其他两种自导引算法。     

基于联立方程模型的货物周转量与GDP的计量关系分析

通过建立联立方程模型,对货物周转量与国内生产总值之间的关系进行定量研究,用Eviews3.1软件对模型采用二阶段最小二乘法（2SLS）进行参数估计,并进行统计意义检验和历史模拟及事后预测,得出模型符合经济意义,可用于货物周转量的预测。     

偏微分方程模型在高速公路交通的应用

偏微分方程中函数的变量是关于时间和空间的,在许多领域中的现象都可以用这样的函数来描述。本文主要以交通模型和人口模型方面的应用来分析和评价。     

探析非线性代数方程组理论引入高等代数课程之教材建设

线性代数方程组理论在科研上具有重要价值,文章分析了非线性代数方程组理论的发展,以及高等代数课程教材现状,认为将非线性代数方程引入到高等代数有其必要性,并对将非线性代数方程引入到高等代数教材的建设提出自己的看法和建议。     

MODEL REFERENCE ADAPTIVE SYSTEM ESTIMATES FOR COUNTING PROCESSES

The adaptive estimation procedure of the model reference adaptive system is modified and applied to counting process models. Maximum likelihood estimates constitute a subclass of the adaptive estimators considered. The adaptive estimator is shown to be strongly consistent and to converge in law to a normal variate. Applications are considered; for example properties of the adaptive estimate are obtained for a periodic intensity model.     

ON ERROR CORRECTION MODELS: SPECIFICATION, INTERPRETATION, ESTIMATION

Abstract. Error Correction Models (ECMs) have proved a popular organising principle in applied econometrics, despite the lack of consensus as to exactly what constitutes their defining characteristic, and the rather limited role that has been given to economic theory by their proponents. This paper uses a historical survey of the evolution of ECMs to explain the alternative specifications and interpretations and proceeds to examine their implications for estimation. The various approaches are illustrated for wage equations by application to UK labour market data 1855–1987. We demonstrate that error correction models impose strong and testable non-linear restrictions on dynamic econometric equations, and that they do not obviate the need for modelling the process of expectations formation. With the exception of a few special cases, both the non-linear restrictions and the modelling of expectations have been ignored by those who have treated ECMs as merely reparameterisations of dynamic linear regression models or vector autoregressions.     

A dynamic multiple equation approach for forecasting PM2.5 pollution in Santiago,Chile

This paper proposes a methodology based on a system of dynamic multiple linear equations that incorporates hourly, daily and annual seasonal characteristics for predicting hourly ${\text{pm}}_{2.5}$ pollution concentrations for 11 meteorological stations in Santiago, Chile. It is demonstrated that the proposed model has the potential to match or even surpass the accuracy of competing nonlinear forecasting models in terms of both fit and predictive ability. In addition, the model is successful at predicting various categories of high concentration events, between 53% and 76% of mid-range events, and around 90% of extreme-range events on average across all stations. This forecasting model is considered a useful tool for helping government authorities to anticipate critical episodes of poor air quality so as to avoid the detrimental economic and health impacts of extreme pollution levels.     

一种改进的遗传算法及其在函数优化中的应用

使用简单遗传算法(SGA)求解线性方程组时,由于易发生"早熟"现象,简单遗传算法求出的数值解误差很大甚至会失真。针对此问题,本文提出了一种改进的遗传算法(IGA),并设计了选择算子,交叉算子和变异算子。为了提高简单遗传算法抗"早熟"的能力,采用遗传算子结合惩罚函数,最佳个体保留以及种群迁移等措施。最后以核磁共振测井数学模型线性化后的大型病态线性方程组为例,对算法进行了测试。实验结果表明:同简单遗传算法相比较,IGA在一定程度上提高了数值解的精度。     

Modelling Strategies for Repeated Multiple Response Data

This article discusses modelling strategies for repeated measurements of multiple response variables. Such data arise in the context of categorical variables where one can select more than one of the categories as the response. We consider each of the multiple responses as a binary outcome and use a marginal (or population‐averaged) modelling approach to analyse its means. Generalized estimating equations are used to account for different correlation structures, both over time and between items. We also discuss an alternative approach using a generalized linear mixed model with conditional interpretations. We illustrate the methods using data from a panel study in Australia called the Household, Income, and Labour Dynamics Survey.     

Legendre小波求解Fredholm-Volterra方程

本文运用Legendre小波求解Fredholm-Volterra方程,建立了Legendre小波的算子矩阵,利用Legendre小波方法求解积分方程的基本思想是将求解积分方程的问题转化为求解一组代数方程组的问题。     

ELUSIVE PERSISTENCE: WAGE AND PRICE RIGIDITIES,THE NEW KEYNESIAN PHILLIPS CURVE AND INFLATION DYNAMICS

Abstract We review the main New Keynesian inflation equations that have arisen as a result of aggregation from individual firms' price rigidities. We find that, on the whole, they cannot account for inflation persistence, a key feature of the empirical dynamics of inflation, and with important policy implications. The only exceptions seem to be when indexation is allowed in price setting or when price stickiness is combined with wage rigidity and staggering.     

中国城市化与经济增长关系实证分析

利用中国1987-2008年的省际面板数据,结合联立方程和分布滞后模型,考察了中国城市化与经济增长之间的相互影响。研究发现:城市化与经济增长的相互促进作用在短期内存在;从累积效应来看,城市化对经济增长呈现显著的负面影响,同时经济增长对城市化也呈现显著的负面影响;从长期来看,中国的经济增长与城市化相互促进的良性循环机制并未形成。