数学代考|计算复杂性理论代写computational complexity theory代考|Agent Based Computational Economics

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计算复杂性理论computational complexity theory的重点是根据资源使用情况对计算问题进行分类,并将这些类别相互联系起来。计算问题是一项由计算机解决的任务。一个计算问题是可以通过机械地应用数学步骤来解决的,比如一个算法。

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我们提供的计算复杂性理论computational complexity theory及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等概率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (Generalized) Linear Models 广义线性模型
  • Statistical Machine Learning 统计机器学习
  • Longitudinal Data Analysis 纵向数据分析
  • Foundations of Data Science 数据科学基础
Schelling's Segregation Model 的图像结果
数学代考|计算复杂性理论代写computational complexity theory代考|Agent Based Computational Economics

数学代考|计算复杂性理论代写computational complexity theory代考|Definition of the Subject

Mainstream economic models typically make the assumption that an entire group of agents, e.g. “investors”, can be modeled with a single “rational representative agent”. While this assumption has proven extremely useful in advancing the science of economics by yielding analytically tractable models, it is clear that the assumption is not realistic: people are different one from the other in their tastes, beliefs, and sophistication, and as many psychological studies have shown, they often deviate from rationality in systematic ways.

Agent Based Computational Economics is a framework allowing economics to expand beyond the realm of the “rational representative agent”. By modeling and simulating the behavior of each agent and the interaction among agents, agent based simulation allows us to investigate the dynamics of complex economic systems with many heterogeneous and not necessarily fully rational agents.

The agent based simulation approach allows economists to investigate systems that can not be studied with the conventional methods. Thus, the following key questions can be addressed: How do heterogeneity and systematic deviations from rationality affect markets? Can these elements explain empirically observed phenomena which are considered “anomalies” in the standard economics literature? How robust are the results obtained with the analytical models? By addressing these questions the agent based simulation approach complements the traditional analytical analysis, and is gradually becoming a standard tool in economic analysis.

数学代考|计算复杂性理论代写computational complexity theory代考|Introduction

For solving the dynamics of two bodies (e.g. stars) with some initial locations and velocities and some law of attraction (e.g. gravitation) there is a well-known analytical solution. However, for a similar system with three bodies there is no known analytical solution. Of course, this does not mean that physicists can’t investigate and predict the behavior of such systems. Knowing the state of the system (i. e. the location, velocity, and acceleration of each body)

at time $t$, allows us to calculate the state of the system an instant later, at time $t+\Delta t$. Thus, starting with the initial conditions we can predict the dynamics of the system by simply simulating the “behavior ” of each element in the system over time.

This powerful and fruitful approach, sometimes called “Microscopic Simulation”, has been adopted by many other branches of science. Its application in economics is best known as “Agent Based Simulation” or “Agent Based Computation”. The advantages of this approach are clear they allow the researcher to go where no analytical models can go. Yet, despite of the advantages, perhaps surprisingly, the agent based approach was not adopted very quickly by economists. Perhaps the main reason for this is that a particular simulation only describes the dynamics of a system with a particular set of parameters and initial conditions. With other parameters and initial conditions the dynamics may be different. So economists may ask: what is the value of conducting simulations if we get very different results with different parameter values? While in physics the parameters (like the gravitational constant) may be known with great accuracy, in economics the parameters (like the risk-aversion coefficient, or for that matter the entire decision-making rule) are typically estimated with substantial error. This is a strong point. Indeed, we would argue that the “art” of agent based simulations is the ability to understand the general dynamics of the system and to draw general conclusions from a finite number of simulations. Of course, one simulation is sufficient as a counterexample to show that a certain result does not hold, but many more simulations are required in order to convince of an alternative general regularity.

This manuscript is intended as an introduction to agent-based computational economics. An introduction to this field has two goals: (i) to explain and to demonstrate the agent-based methodology in economics, stressing the advantages and disadvantages of this approach relative to the alternative purely analytical methodology, and (ii) to review studies published in this area. The emphasis in this paper will be on the first goal. While Sect. “Some of the Pioneering Studies” does provide a brief review of some of the cornerstone studies in this area, more comprehensive reviews can be found in $[19,24,32,39,40]$, on which part of Sect. “Some of the Pioneering Studies” is based. A comprehensive review of the many papers employing agent based computational models in economics will go far beyond the scope of this article. To achieve goal (i) above, in Sect. “Illustration with the LLS Model” we will focus on one particular model of the stock market in some detail. Section “Summary and Future Directions” concludes with some thoughts about the future of the field.

数学代考|计算复杂性理论代写computational complexity theory代考|Schelling’s Segregation Model

Schelling’s [36] classical segregation model is one of the earliest models of population dynamics. Schelling’s model is not intended as a realistic tool for studying the actual dynamics of specific communities as it ignores economic, real-estate and cultural factors. Rather, the aim of this very simplified model is to explain the emergence of macroscopic single-race neighborhoods even when individuals are not racists. More precisely, Schelling found that the collective effect of neighborhood racial segregation results even from individual behavior that presents only a very mild preference for same-color neighbors. For instance, even the minimal requirement by each individual of having (at least) one neighbor belonging to ones’ own race leads to the segregation effect.

The agent based simulation starts with a square mesh, or lattice, (representing a town) which is composed of cells (representing houses). On these cells reside agents which are either “blue” or “green” (the different races). The crucial parameter is the minimal percentage of same-color neighbors that each agent requires. Each agent, in his turn, examines the color of all his neighbors. If the percentage of neighbors belonging to his own group is above the “minimal percentage”, the agent does nothing. If the percentage of neighbors of his own color is less then the minimal percentage, the agent moves to the closest unoccupied cell. The agent then examines the color of the neighbors of the new location and acts accordingly (moves if the number of neighbors of his own color is below the minimal percentage and stays there otherwise). This goes on until the agent is finally located at a cite in which the minimal percentage condition holds. After a while, however, it might happen that following the moves of the other agents, the minimal percentage condition ceases to be fulfilled and then the agent starts moving again until he finds an appropriate cell. As mentioned above, the main result is that even for very mild individual preferences for same-color neighbors, after some time the entire system displays a very high level of segregation.

A more modern, developed and sophisticated reincarnation of these ideas is the Sugarscape environment described by Epstein and Axtell [6]. The model considers a population of moving, feeding, pairing, procreating, trading, warring agents and displays various qualitative collective events which their populations incur. By employing agent based simulation one can study the macroscopic results induced by the agents’ individual behavior.

Schelling's Segregation Model 的图像结果
数学代考|计算复杂性理论代写computational complexity theory代考|Agent Based Computational Economics

计算复杂性理论代写

数学代考|计算复杂性理论代写computational complexity theory代考|Definition of the Subject

主流经济模型通常假设整个代理组,例如“投资者”,可以用单个“理性代表代理”建模。虽然这一假设已被证明通过产生易于分析的模型在推进经济学科学方面非常有用,但很明显,该假设是不现实的:人们在品味、信仰和成熟度方面与其他人不同,并且与许多心理学研究一样已经表明,他们经常以系统的方式偏离理性。

基于代理的计算经济学是一个允许经济学扩展到“理性代表代理”领域之外的框架。通过对每个代理的行为以及代理之间的交互进行建模和模拟,基于代理的模拟使我们能够研究具有许多异构且不一定完全理性的代理的复杂经济系统的动态。

基于代理的模拟方法允许经济学家研究无法用传统方法研究的系统。因此,可以解决以下关键问题:异质性和对理性的系统性偏差如何影响市场?这些要素能否解释在标准经济学文献中被视为“异常”的经验观察现象?使用分析模型获得的结果有多稳健?通过解决这些问题,基于代理的模拟方法补充了传统的分析分析,并逐渐成为经济分析的标准工具。

数学代考|计算复杂性理论代写computational complexity theory代考|Introduction

为了求解具有一些初始位置和速度以及一些吸引力法则(例如万有引力)的两个物体(例如恒星)的动力学,有一个众所周知的解析解。但是,对于具有三个主体的类似系统,没有已知的解析解。当然,这并不意味着物理学家无法调查和预测此类系统的行为。了解系统的状态(即每个物体的位置、速度和加速度)

有时吨, 允许我们稍后计算系统的状态吨+Δ吨. 因此,从初始条件开始,我们可以通过简单地模拟系统中每个元素随时间的“行为”来预测系统的动态。

这种强大而富有成效的方法,有时被称为“微观模拟”,已被许多其他科学分支采用。它在经济学中的应用以“基于代理的模拟”或“基于代理的计算”而闻名。这种方法的优点很明显,它们允许研究人员去没有分析模型可以去的地方。然而,尽管有这些优势,也许令人惊讶的是,基于代理的方法并没有很快被经济学家采用。造成这种情况的主要原因可能是特定的模拟仅描述了具有一组特定参数和初始条件的系统的动力学。对于其他参数和初始条件,动态可能会有所不同。所以经济学家可能会问:如果我们用不同的参数值得到非常不同的结果,那么进行模拟的价值是什么?虽然在物理学中可以非常准确地知道参数(如引力常数),但在经济学中,参数(如风险规避系数,或就此而言,整个决策规则)的估计通常存在很大误差。这是一个强项。事实上,我们认为基于代理的模拟的“艺术”是能够理解系统的一般动态并从有限数量的模拟中得出一般结论的能力。当然,一个模拟作为反例足以表明某个结果不成立,但需要更多的模拟才能说服另一种一般规律。

这份手稿旨在介绍基于代理的计算经济学。对该领域的介绍有两个目标:(i)解释和展示经济学中基于代理的方法,强调这种方法相对于替代纯分析方法的优缺点,以及(ii)回顾发表在这片区域。本文的重点将放在第一个目标上。虽然教派。“一些开创性研究”确实提供了对该领域的一些基石研究的简要回顾,更全面的回顾可以在[19,24,32,39,40],在教派的哪个部分。“一些开创性研究”是根据。对经济学中使用基于代理的计算模型的许多论文进行全面回顾将远远超出本文的范围。为了实现上述目标 (i),在 Sect. 在“LLS 模型的说明”中,我们将重点关注一种特定的股票市场模型。“总结和未来方向”部分总结了对该领域未来的一些想法。

数学代考|计算复杂性理论代写computational complexity theory代考|Schelling’s Segregation Model

Schelling 的 [36] 经典隔离模型是最早的种群动态模型之一。Schelling 的模型并非旨在作为研究特定社区实际动态的现实工具,因为它忽略了经济、房地产和文化因素。相反,这个非常简化的模型的目的是解释宏观单一种族社区的出现,即使个人不是种族主义者。更准确地说,谢林发现,邻里种族隔离的集体效应甚至来自对同色邻居仅表现出非常温和的偏好的个人行为。例如,即使每个人(至少)有一个属于自己种族的邻居的最低要求也会导致隔离效应。

基于代理的模拟从由单元(代表房屋)组成的方形网格或格子(代表城镇)开始。在这些细胞上驻留“蓝色”或“绿色”(不同种族)的代理。关键参数是每个代理所需的同色邻居的最小百分比。每个代理人轮流检查他所有邻居的颜色。如果属于他自己组的邻居的百分比高于“最小百分比”,则代理什么也不做。如果他自己颜色的邻居的百分比小于最小百分比,则代理移动到最近的未占用单元格。然后代理检查新位置的邻居的颜色并采取相应的行动(如果他自己颜色的邻居的数量低于最小百分比,则移动,否则保持在那里)。这种情况一直持续到代理最终位于满足最小百分比条件的引用处。然而,一段时间后,可能会发生以下情况:随着其他智能体的移动,最小百分比条件不再满足,然后智能体再次开始移动,直到找到合适的单元格。如上所述,主要结果是即使对于同色邻居的非常温和的个人偏好,一段时间后整个系统也会显示出非常高的隔离水平。

Epstein 和 Axtell [6] 描述的 Sugarscape 环境是这些想法的更现代、更发达和更复杂的转世。该模型考虑了移动、喂养、配对、繁殖、交易、交战代理的群体,并显示了他们的群体发生的各种定性集体事件。通过采用基于代理的模拟,可以研究由代理的个体行为引起的宏观结果。

数学代考|计算复杂性理论代写computatiknal complexity theory代考 请认准statistics-lab™

统计代写请认准statistics-lab™. statistics-lab™为您的留学生涯保驾护航。

金融工程代写

金融工程是使用数学技术来解决金融问题。金融工程使用计算机科学、统计学、经济学和应用数学领域的工具和知识来解决当前的金融问题,以及设计新的和创新的金融产品。

非参数统计代写

非参数统计指的是一种统计方法,其中不假设数据来自于由少数参数决定的规定模型;这种模型的例子包括正态分布模型和线性回归模型。

广义线性模型代考

广义线性模型(GLM)归属统计学领域,是一种应用灵活的线性回归模型。该模型允许因变量的偏差分布有除了正态分布之外的其它分布。

术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。

有限元方法代写

有限元方法(FEM)是一种流行的方法,用于数值解决工程和数学建模中出现的微分方程。典型的问题领域包括结构分析、传热、流体流动、质量运输和电磁势等传统领域。

有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。

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随机分析代写


随机微积分是数学的一个分支,对随机过程进行操作。它允许为随机过程的积分定义一个关于随机过程的一致的积分理论。这个领域是由日本数学家伊藤清在第二次世界大战期间创建并开始的。

时间序列分析代写

随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。

回归分析代写

多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。

MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中,其中问题和解决方案以熟悉的数学符号表示。典型用途包括:数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发,包括图形用户界面构建MATLAB 是一个交互式系统,其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题,尤其是那些具有矩阵和向量公式的问题,而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问,这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展,得到了许多用户的投入。在大学环境中,它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域,MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要,工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数(M 文件)的综合集合,可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。

R语言代写问卷设计与分析代写
PYTHON代写回归分析与线性模型代写
MATLAB代写方差分析与试验设计代写
STATA代写机器学习/统计学习代写
SPSS代写计量经济学代写
EVIEWS代写时间序列分析代写
EXCEL代写深度学习代写
SQL代写各种数据建模与可视化代写

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