### 数学代考|计算复杂性理论代写computational complexity theory代考|Full Spectrum of EMB Investors

statistics-lab™ 为您的留学生涯保驾护航 在代写计算复杂性理论computational complexity theory方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写计算复杂性理论computational complexity theory代写方面经验极为丰富，各种代写计算复杂性理论相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (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|Full Spectrum of EMB Investors

Full Spectrum of EMB Investors Up to this point we have analyzed markets with at most three different subpopulations (one RII population and two EMB populations). The market dynamics we found displayed the empirically observed market anomalies, but they were unrealistic in the magnitude, frequency, and semi-predictability of booms and crashes. In reality, we would expect not only two or three investor types, but rather an entire spectrum of investors. In this section we consider a model with a full spectrum of different EMB investors. It turns out that more is different. When there is an entire range of investors, the price dynamics become realistic: booms and crashes are not periodic or predictable, and they are also less frequent and dramatic. At the same time, we still obtain all of the market anomalies described before.

In this model each investor has a different number of ex-post observations which he utilizes to estimate the exante distribution. Namely, investor $i$ looks at the set of the $m^{i}$ most recent returns on the stock, and we assume that $m^{i}$ is distributed in the population according to a trun-

cated normal distribution with average $\tilde{m}$ and standard deviation $\sigma_{m}$ (as $m \leq 0$ is meaningless, the distribution is truncated at $m=0$ ).

Figure 8 shows the price pattern of a typical simulation of this model. In this simulation $90 \%$ of the investors are RII, and the remaining $10 \%$ are heterogeneous EMB investors with $\bar{m}=40$, and $\sigma_{m}=10$. The price pattern seems very realistic with “smoother” and more irregular cycles. Crashes are dramatic, but infrequent and unpredictable.

The heterogeneous EMB population model generates the following empirically observed market phenomena:
Return Autocorrelation: Momentum and Mean-Reversion In the heterogeneous EMB population model trends are generated by the same positive feedback mechanism that generated cycles in the homogeneous case: high (low) returns tend to make the EMB investors more (less) aggressive, this generates more high (low) returns, etc. The difference between the two cases is that in the heterogeneous case there is a very complicated interaction between all the different investor sub-populations and as a result there are no distinct regular cycles, but rather, smoother and more irregular trends. There is no single cycle length the dynamics are a combination of many different cycles. This makes the autocorrelation pattern also smoother and more continuous. The return autocorrelations in the heterogeneous model are shown in Fig. 9. This autocorrelation pattern conforms with the empirical findings. In the short-run (lags 1-4) the autocorrelation is positive – this is the empirically documented phenomena known as momentum: in the short-run, high returns tend to be fol-lowed by more high returns, and low returns tend to be followed by more low returns. In the longer-run (lags 5-13) the autocorrelation is negative, which is known as meanreversion. For even longer lags the autocorrelation eventually tends to zero. The short-run momentum, longerrun mean-reversion, and eventual diminishing autocorrelation creates the general “U-shape” which is found in empirical studies $[7,13,31]$ and which is seen in Fig. $9 .$

## 数学代考|计算复杂性理论代写computational complexity theory代考|Discussion of the LLS Results

Discussion of the LLS Results The LLS model is an Agent Based Simulation model of the stock market which incorporates some of the fundamental experimental findings regarding the behavior of investors. The main nonstandard assumption of the model is that there is a small minority of investors in the market who are uninformed about the dividend process and who believe in market efficiency. The investment decision of these investors is reduced to the optimal diversification between the stock and the bond.

The LLS model generates many of the empirically documented market phenomena which are hard to explain in the analytical rational-representative-agent framework. These phenomena are:

• Short term momentum;
• Longer term mean reversion;
• Excess volatility;
• Positive correlation between volume and contemporaneous absolute returns;
• Positive correlation between volume and lagged absolute returns;
• Endogenous market crashes.
The fact that so many “puzzles” are explained with a simple model built on a small number of empirically documented behavioral elements leads us to suspect that these behavioral elements are very important in understanding the workings of the market. This is especially true in light of the observations that a very small minority of the nonstandard bounded-rational investors can have a dramatic influence on the market, and that these investors are not wiped out by the majority of rational investors.

## 数学代考|计算复杂性理论代写computational complexity theory代考|Summary and Future Directions

Standard economic models typically describe a world of homogeneous rational agents. This approach is the foundation of most of our present day knowledge in economic theory. With the Agent Based Simulation approach we can investigate a much more complex and “messy” world with different agent types, who employ different strategies to try to survive and prosper in a market with structural uncertainty. Agents can learn over time, from their own experience and from their observation about the performance of other agents. They co-evolve over time and as they do so, the market dynamics change continuously. This is a world view closer to biology, than it is to the “clean” realm of physical laws which classical economics has aspired to.
The Agent Based approach should not and can not replace the standard analytical economic approach. Rather, these two methodologies support and complement each other: When an analytical model is developed, it should become standard practice to examine the robustness of the model’s results with agent based simulations. Similarly, when results emerge from agent based simulation, one should try to understand their origin and their generality, not only by running many simulations, but also by trying to capture the essence of the results in a simplified analytical setting (if possible).

Although the first steps in economic agent based simulations were made decades ago, economics has been slow and cautious to adopt this new methodology. Only in recent years has this field begun to bloom. It is my belief and hope that the agent based approach will prove as fruitful in economics as it has been in so many other branches of science.

## 数学代考|计算复杂性理论代写computational complexity theory代考|Full Spectrum of EMB Investors

EMB 投资者的全谱 到目前为止，我们已经分析了最多包含三个不同子群体（一个 RII 群体和两个 EMB 群体）的市场。我们发现的市场动态显示了经验观察到的市场异常，但它们在繁荣和崩溃的幅度、频率和半可预测性方面是不切实际的。实际上，我们预计的不仅是两种或三种投资者类型，而是整个范围的投资者。在本节中，我们考虑一个包含各种不同 EMB 投资者的模型。事实证明，更多是不同的。当有一个完整的投资者范围时，价格动态变得现实：繁荣和崩溃不是周期性的或可预测的，而且它们也不那么频繁和剧烈。同时，我们仍然获得了之前描述的所有市场异常。

## 数学代考|计算复杂性理论代写computational complexity theory代考|Discussion of the LLS Results

LLS 结果的讨论 LLS 模型是一种基于代理的股票市场模拟模型，它结合了一些关于投资者行为的基本实验结果。该模型的主要非标准假设是市场上有少数投资者不了解股息过程并相信市场效率。这些投资者的投资决策被简化为股票和债券之间的最佳多元化。

LLS 模型产生了许多在分析理性-代表-代理框架中难以解释的经验记录的市场现象。这些现象是：

• 短期动量；
• 长期均值回归；
• 过度波动；
• 交易量大；
• 成交量与同期绝对收益呈正相关；
• 交易量与滞后绝对收益呈正相关；
• 内生市场崩盘。
如此多的“谜题”是用一个建立在少数经验证明的行为元素上的简单模型来解释的，这一事实使我们怀疑这些行为元素对于理解市场运作非常重要。鉴于极少数非标准有限理性投资者可以对市场产生巨大影响，并且这些投资者并未被大多数理性投资者淘汰，这一点尤其正确。

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## 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。