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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
数学代考|计算复杂性理论代写computational complexity theory代考|The Kim and Markowitz Portfolio Insurers Model
Harry Markowitz is very well known for being one of the founders of modern portfolio theory, a contribution for which he has received the Nobel Prize in economics. It is less well known, however, that Markowitz is also one of the pioneers in employing agent based simulations in economics.
During the October 1987 crash markets all over the globe plummeted by more than $20 \%$ within a few days. The surprising fact about this crash is that it appeared to be spontaneous – it was not triggered by any obvious event. Following the 1987 crash researchers started to look for endogenous market features, rather than external forces, as sources of price variation. The Kim-Markowitz [15] model explains the 1987 crash as resulting from investors? “Constant Proportion Portfolio Insurance” (CPPI) policy. Kim and Markowitz proposed that market instabilities arise as a consequence of the individual insurers’ efforts to cut their losses by selling once the stock prices are going down.
The Kim Markowitz agent based model involves two groups of individual investors: rebalancers and insurers (CPPI investors). The rebalancers are aiming to keep a constant composition of their portfolio, while the insurers make the appropriate operations to insure that their eventual losses will not exceed a certain fraction of the investment per time period.
The rebalancers act to keep a portfolio structure with (for instance) half of their wealth in cash and half in stocks. If the stock price rises, then the stocks weight in the portfolio will increase and the rebalancers will sell shares until the shares again constitute $50 \%$ of the portfolio. If the stock price decreases, then the value of the shares in the portfolio decreases, and the rebalancers will buy shares until the stock again constitutes $50 \%$ of the portfolio. Thus, the rebalancers have a stabilizing influence on the market by selling when the market rises and buying when the market falls.
A typical CPPI investor has as his/her main objective not to lose more than (for instance) $25 \%$ of his initial wealth during a quarter, which consists of 65 trading days. Thus, he aims to insure that at each cycle $75 \%$ of the initial wealth is out of reasonable risk. To this effect, he assumes that the current value of the stock will not fall in one day by more than a factor of 2 . The result is that he always keeps in stock twice the difference between the present wealth and $75 \%$ of the initial wealth (which he had at the beginning of the 65 days investing period). This determines the amount the CPPI agent is bidding or offering at each stage. Obviously, after a price fall, the amount he wants to keep
in stocks will fall and the CPPI investor will sell and further destabilize the market. After an increase in the prices (and personal wealth) the amount the CPPI agent wants to keep in shares will increase: he will buy, and may support a price bubble.
The simulations reveal that even a relatively small fraction of CPPI investors (i. e. less than $50 \%$ ) is enough to destabilize the market, and crashes and booms are observed. Hence, the claim of Kim and Markowitz that the CPPI policy may be responsible for the 1987 crash is supported by the agent based simulations. Various variants of this model were studied intensively by Egenter, Lux and Stauffer [5] who find that the price time evolution becomes unrealistically periodic for a large number of investors (the periodicity seems related with the fixed 65 days quarter and is significantly diminished if the 65 day period begins on a different date for each investor).
数学代考|计算复杂性理论代写computational complexity theory代考|The Arthur, Holland, Lebaron, Palmer and Tayler Stock Market Model
Palmer, Arthur, Holland, Lebaron and Tayler [30] and Arthur, Holland, Lebaron, Palmer and Tayler 3 construct an agent based simulation model that is focused on the concept of co-evolution. Each investor adapts his/her investment strategy such as to maximally exploit the market dynamics generated by the investment strategies of all others investors. This leads to an ever-evolving market, driven endogenously by the everchanging strategies of the investors.
The main objective of AHLPT is to prove that market fluctuations may be induced by this endogenous coevolution, rather than by exogenous events. Moreover, AHLPT study the various regimes of the system: the regime in which rational fundamentalist strategies are dominating vs. the regime in which investors start developing strategies based on technical trading. In the technical trading regime, if some of the investors follow fundamentalist strategies, they may be punished rather than rewarded by the market. AHLPT also study the relation between the various strategies (fundamentals vs. technical) and the volatility properties of the market (clustering, excess volatility, volume-volatility correlations, etc.).
In the first paper quoted above, the authors simulated a single stock and further limited the bid/offer decision to a ternary choice of: i) bid to buy one share, ii) offer to sell one share, or: iii) do nothing. Each agent had a collection of rules which described how he should behave (i, ii or iii) in various market conditions. If the current market conditions were not covered by any of the rules, the default was to do nothing. If more than one rule applied in a certain
market condition, the rule to act upon was chosen probabilistically according to the “strengths” of the applicable rules. The “strength” of each rule was determined according to the rule’s past performance: rules that “worked” became “stronger”. Thus, if a certain rule performed well, it became more likely to be used again.
The price is updated proportionally to the relative excess of offers over demands. In [3], the rules were used to predict future prices. The price prediction was then transformed into a buy/sell order through the use of a Constant Absolute Risk Aversion (CARA) utility function. The use of CARA utility leads to demands which do not depend on the investor’s wealth.
The heart of the AHLPT dynamics are the trading rules. In particular, the authors differentiate between “fundamental” rules and “technical” rules, and study their relative strength in various market regimes. For instance, $a^{\text {“fundamental }}$ ” rule may require a market conditions of the type:
$$
\frac{\text { dividend }}{\text { current price }}>0.04
$$
in order to be applied. A “technical” rule may be triggered if the market fulfills a condition of the type:
current price $>10$-period moving-average of past prices.
The rules undergo genetic dynamics: the weakest rules are substituted periodically by copies of the strongest rules and all the rules undergo random mutations (or even versions of “sexual” crossovers: new rules are formed by combining parts from 2 different rules). The genetic dynamics of the trading rules represent investors’learning: new rules represent new trading strategies. Investors examine new strategies, and adopt those which tend to work best. The main results of this model are:
For a Few Agents, a Small Number of Rules, and Small Dividend Changes
- The price converges towards an equilibrium price which is close to the fundamental value.
- Trading volume is low.
- There are no bubbles, crashes or anomalies.
- Agents follow homogeneous simple fundamentalist rules.
数学代考|计算复杂性理论代写computational complexity theory代考|The Lux and Lux and Marchesi Model
Lux [27] and Lux and Marchesi [28] propose a model to endogenously explain the heavy tail distribution of returns and the clustering of volatility. Both of these phenomena emerge in the Lux model as soon as one assumes that in addition to the fundamentalists there are also chartists in the model. Lux and Marchesi [28] further divide the chartists into optimists (buyers) and pessimists (sellers). The market fluctuations are driven and amplified by the fluctuations in the various populations: chartists converting into fundamentalists, pessimists into optimists, etc.
In the Lux and Marchesi model the stock’s fundamental value is exogenously determined. The fluctuations of the fundamental value are inputted exogenously as a white noise process in the logarithm of the value. The market price is determined by investors’ demands and by the market clearance condition.
Lux and Marchesi consider three types of traders:
- Fundamentalists observe the fundamental value of the stock. They anticipate that the price will eventually converge to the fundamental value, and their demand for shares is proportional to the difference between the market price and the fundamental value.
- Chartists look more at the present trends in the market price rather than at fundamental economic values; the chartists are divided into
- Optimists (they buy a fixed amount of shares per unit time)
- Pessimists (they sell shares).
Transitions between these three groups (optimists, pessimists, fundamentalists) happen with probabilities depending on the market dynamics and on the present numbers of traders in each of the three classes:The transition probabilities of chartists depend on the majority opinion (through an “opinion index” measuring the relative number of optimists minus the relative number of pessimists) and on the actual price trend (the current time derivative of the current market price), which determines the relative profit of the various strategies. - The fundamentalists decide to turn into chartists if the profits of the later become significantly larger than their own, and vice versa (the detailed formulae used by Lux and Marchesi are inspired from the exponential transition probabilities governing statistical mechanics physical systems).
- The main results of the model are:
- No long-term deviations between the current market price and the fundamental price are observed.
- The deviations from the fundamental price, which do occur, are unsystematic.
- In spite of the fact that the variations of the fundamental price are normally distributed, the variations of the market price (the market returns) are not. In particular the returns exhibit a frequency of extreme events which is higher than expected for a normal distribution. The authors emphasize the amplification role of the market that transforms the input normal distribution of the fundamental value variations into a leptokurtotic (heavy tailed) distribution of price variation, which is encountered in the actual financial data.
- clustering of volatility.
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|The Kim and Markowitz Portfolio Insurers Model
Harry Markowitz 以现代投资组合理论的创始人之一而闻名，他因此获得了诺贝尔经济学奖。然而，鲜为人知的是，马科维茨也是在经济学中采用基于代理的模拟的先驱之一。
在 1987 年 10 月的崩盘期间，全球市场暴跌超过20%几天之内。关于这次崩溃的令人惊讶的事实是，它似乎是自发的——它不是由任何明显的事件触发的。1987 年崩盘之后，研究人员开始寻找内生的市场特征，而不是外部力量，作为价格变化的来源。Kim-Markowitz [15] 模型将 1987 年的崩盘解释为投资者造成的？“固定比例投资组合保险”（CPPI）政策。Kim 和 Markowitz 提出，市场不稳定是由于个别保险公司在股价下跌时通过出售来减少损失的努力的结果。
基于 Kim Markowitz 代理的模型涉及两组个人投资者：再平衡者和保险公司（CPPI 投资者）。再平衡者的目标是保持其投资组合的恒定组成，而保险公司则进行适当的操作以确保其最终损失不会超过每个时期投资的一定比例。
再平衡者采取行动保持投资组合结构，例如，他们一半的财富是现金，一半是股票。如果股价上涨，则投资组合中的股票权重将增加，再平衡者将出售股票，直到股票再次构成50%的投资组合。如果股价下跌，那么投资组合中股票的价值就会下降，再平衡者将购买股票，直到股票再次构成50%的投资组合。因此，再平衡器通过在市场上涨时卖出并在市场下跌时买入来对市场产生稳定影响。
典型的 CPPI 投资者的主要目标是不损失超过（例如）25%他在一个季度（包括 65 个交易日）内的初始财富。因此，他的目标是确保在每个周期75%的初始财富是出于合理的风险。为此，他假设股票的当前价值不会在一天内下跌超过 2 倍。结果是他的存货总是两倍于现在的财富和75%初始财富（他在 65 天投资期开始时拥有）。这决定了 CPPI 代理在每个阶段的投标或报价金额。显然，在价格下跌之后，他想要保留的数量
股票将下跌，CPPI 投资者将抛售并进一步破坏市场稳定。在价格（和个人财富）上涨之后，CPPI 代理人想要持有的股票数量将会增加：他会购买，并可能支持价格泡沫。
模拟表明，即使是相对较小的 CPPI 投资者（即少于50%) 足以破坏市场的稳定，并观察到崩盘和繁荣。因此，Kim 和 Markowitz 声称 CPPI 政策可能是 1987 年崩溃的原因得到了基于代理的模拟的支持。Egenter、Lux 和 Stauffer [5] 对该模型的各种变体进行了深入研究，他们发现对于大量投资者而言，价格时间演变变得不切实际的周期性（周期性似乎与固定的 65 天季度有关，如果每个投资者的 65 天期限从不同的日期开始）。
数学代考|计算复杂性理论代写computational complexity theory代考|The Arthur, Holland, Lebaron, Palmer and Tayler Stock Market Model
Palmer、Arthur、Holland、Lebaron 和 Tayler [30] 以及 Arthur、Holland、Lebaron、Palmer 和 Tayler 3构建了一个基于代理的仿真模型，该模型专注于协同进化的概念。每个投资者都会调整他/她的投资策略，以最大限度地利用所有其他投资者的投资策略产生的市场动态。这导致了一个不断发展的市场，由投资者不断变化的策略内生驱动。
AHLPT 的主要目标是证明市场波动可能是由这种内生的协同进化引起的，而不是由外生事件引起的。此外，AHLPT 研究了系统的各种制度：理性的原教旨主义策略占主导地位的制度与投资者开始基于技术交易制定策略的制度。在技术交易体系中，如果部分投资者遵循原教旨主义策略，他们可能会受到市场的惩罚而不是奖励。AHLPT 还研究各种策略（基本面与技术面）与市场波动性特性（聚类、过度波动、交易量-波动率相关性等）之间的关系。
在上面引用的第一篇论文中，作者模拟了一只股票，并进一步将买入/卖出决策限制为三元选择：i）买入一股，ii）卖出一股，或：iii）什么都不做。每个代理人都有一组规则，描述了他在各种市场条件下应该如何表现（i、ii 或 iii）。如果任何规则均未涵盖当前的市场状况，则默认为不采取任何行动。如果在某个特定应用中应用了多个规则
在市场条件下，要采取行动的规则是根据适用规则的“优势”概率性地选择的。每个规则的“强度”是根据该规则过去的表现来确定的：“有效”的规则变得“更强”。因此，如果某个规则表现良好，它就更有可能再次被使用。
价格根据报价超过需求的相对过剩比例进行更新。在 [3] 中，这些规则用于预测未来价格。然后通过使用恒定绝对风险厌恶 (CARA) 效用函数将价格预测转换为买入/卖出订单。CARA 公用事业的使用导致了不依赖于投资者财富的需求。
AHLPT 动态的核心是交易规则。特别是，作者区分了“基本”规则和“技术”规则，并研究了它们在各种市场制度中的相对优势。例如，一种“基本的 ”规则可能需要以下类型的市场条件：
股利 目前的价格 >0.04
为了被应用。如果市场满足以下类型的条件，则可能会触发“技术”规则：
当前价格>10- 过去价格的周期移动平均线。
规则经历遗传动力学：最弱的规则被最强规则的副本定期替换，所有规则都经历随机突变（甚至是“性”交叉的版本：新规则是通过组合来自 2 个不同规则的部分形成的）。交易规则的遗传动力代表了投资者的学习：新规则代表新的交易策略。投资者检查新策略，并采用那些往往效果最好的策略。该模型的主要结果是：
对于少数代理人、少量规则和少量股息变化
- 价格趋于接近基本价值的均衡价格。
- 交易量低。
- 没有气泡、崩溃或异常。
- 代理人遵循同质的简单原教旨主义规则。
数学代考|计算复杂性理论代写computational complexity theory代考|The Lux and Lux and Marchesi Model
Lux [27] 和 Lux 和 Marchesi [28] 提出了一个模型来内生地解释收益的重尾分布和波动性的聚类。一旦人们假设除了原教旨主义者之外，模型中还有图表主义者，这两种现象就会出现在勒克斯模型中。Lux 和 Marchesi [28] 进一步将图表分析师分为乐观主义者（买家）和悲观主义者（卖家）。市场波动是由不同人群的波动驱动和放大的：图表主义者转变为原教旨主义者，悲观主义者转变为乐观主义者，等等。
在 Lux 和 Marchesi 模型中，股票的基本价值是外生决定的。基值的波动作为白噪声过程以值的对数形式外生地输入。市场价格由投资者的需求和市场出清情况决定。
Lux 和 Marchesi 考虑了三种类型的交易者：
- 基本面主义者观察股票的基本价值。他们预计价格最终会收敛到基本价值，他们对股票的需求与市场价格和基本价值之间的差额成正比。
- 图表专家更多地关注市场价格的当前趋势，而不是基本经济价值；图表专家分为
- 乐观主义者（他们每单位时间购买固定数量的股票）
- 悲观主义者（他们出售股票）。
这三组（乐观主义者、悲观主义者、基本面主义者）之间的转变发生的概率取决于市场动态和三个类别中每个类别的当前交易者数量：图表师的转变概率取决于多数意见（通过“意见指数” ”衡量乐观者的相对数量减去悲观者的相对数量）和实际价格趋势（当前市场价格的当前时间导数），这决定了各种策略的相对利润。 - 如果后者的利润明显大于他们自己的利润，则原教旨主义者决定变成图表主义者，反之亦然（Lux 和 Marchesi 使用的详细公式的灵感来自于管理统计力学物理系统的指数转换概率）。
- 该模型的主要结果是：
- 没有观察到当前市场价格与基本价格之间的长期偏差。
- 确实发生的与基本价格的偏差是非系统性的。
- 尽管基本价格的变化是正态分布的，但市场价格（市场收益）的变化却不是。特别是回报表现出极端事件的频率高于正态分布的预期。作者强调了市场的放大作用，它将基本价值变化的输入正态分布转换为价格变化的细峰（重尾）分布，这在实际金融数据中会遇到。
- 波动性的聚类。
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，工具箱允许您学习和应用专业技术。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。