转变点在经济、金融、计量经济学中的数学建模——结构性变化的研究及其应用-沈卉卉.docx
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1、华中科技大学 硕士学位论文 转变点在经济、金融、计量经济学中的数学建模 一 结构性变 化的研究及其应用 姓名:沈卉卉 申请学位级别:硕士 专业:概率论与数理统计 指导教师:万建平 20060408 华中科技大学硕士学位论文 摘要 近些年来,转变点问题一直是统计学前沿研宄的热点问题之一。它既在理论上 有其深刻的意义而又具有重要的应用价值,同时已应用于很多不同学科,如:在经济 学、金融学、医学、物理学、地理学、文学等,尤其在经济学和金融学方面有广泛 的应用。 转变点问题无论在理论方面还是在应用方面都取得了极有价值的研宄成果,然 而,还存在一些内容值得我们深入研宄。 在经济飞速发展的现代社会,需要处
2、理经济、金融的问题也越来越多,本文将 转变点应用到我国居民消费与收入的线性回归模型中来检测它们之间的线性关系是 否发生变化,采用将二分分段法和 Schwarz信息准则有效的结合起来,给出了一个 简单而迅速的方法准确找出多个转变点的数量及其位置,克服了传统方法检测单个 转变点模型的弊端。在处理经济模型时,几何分布滞后模型普遍存在着 Koyck变换 所带来的随机误差项的自相关及 随机误差项与解释变量之间的相关问题,将工具变 量法和广义差分法相结合的估计方法,就可以很好的克服以上问题,从而更准确的 进行数学建模,解释经济问题,制定相应的经济措施。 随着金融证券市场的交易规模日趋扩大,价格风险也将剧增
3、。金融市场风险也 无法回避,股票指数期货正是一种有效的规避系统风险的工具。股票指数期货作为 一种衍生金融工具,具有套期保值、套利和投机三种功能。其中,套期保值是最基本 的投资策略。本文针对套期保值用来规避市场风险,给出另外一种分析方法。其明 显的不同,它是通过现货市场的价格与期货市场的价格基差来判断,然后在两个不 同市场上做交易,达到在两个市场都稳定盈利,来规避风险。而传统做法是通过在 期货市场买卖期货合约来盈利,以弥补现货市场的亏损。此外,本文对不对称信息 的环境下的具有私人信息道德风险的委托一代理人模型的合约问题,进行讨论的方 法值得推广,对于最优激励合同的设计,具有很好的实用价值和研宄意
4、义。 关 键 词 : 转变点几何分布滞后模型股票指数期货委托一代理模型 Schwarz信息准则 Koyck变 换 套 期 保 值 尤 以 如 - 加 r条件 I 华中科技大学硕士学位论文 Abstract This recent year, the problem about change point is always one of the hot issues in the leading field of the research of statistics. There is profound signification in theory and there is important
5、 value of the application. At the same time, it is already applied to various subjects. Such as economics, finance, iatrology, physics, geography, literature. Especially, in the economic and financial fields the application of change point is sufficiently abroad. We have got research fruit full of v
6、alue about Change Point not only in theory but also in application in the past few years. But there is something worthy of our further research. It requires dealing with more and more the economic and financial problems in the modern society of developing at very fast speed in economy. In this paper
7、, we apply the change point to the linear regression about the consumption and income of resident in our country, and examine the linear relation between the consumption and income whether they are changed. And we gave a simple and quick method that we combined validly the binary segmentation with S
8、chwarz Information Criterion to find the amounts and the positions of the change points correctly. It can overcome the defect of checking up only one change point in the traditional method. When dealing with economic model, it exists universally two problems that are the autocorrelations of residual
9、 error and the correlations between residual errors by Koyck transformation in Geometric Distributed Lag Model. In allusion to the simultaneity of the two problems, we give a particular estimation method that we combine the method of Instrument List with the method of Generalized Difference. Then we
10、 can make mathematical model exactly, and explain economic question, take the corresponding economic measures. With the enlarging of the scale of the financial trade in the securities business increasingly, the risk of price is also increasing. The risk of the money market is incapably avoidable, th
11、e stock index futures iII 华中科技大学硕士学位论文 Stock index futures have three functions of hedging arbitrage and speculate as a derivation financial tool. Thereinto, hedging is the most basic investments strategy. In this paper, in allusion to hedging, which is used to avoid market risk. We give another ini
12、mitable method to analyze. Different obviously, it is estimated by price difference between the market of merchandise on hand and futures. Then it is traded in two different markets, in order to payoff steadily in the two markets to avoid the risk. But the traditional method is that we payoff by mer
13、chandising futures agreements in futures markets to offset the loss in the market of merchandise on hand. Besides, we go to discuss the question about the contract that is moral hazard with private information under the circumstance of asymmetric information between the principal and the agent, and
14、the method of discussing the question is deserved commending and generalizing. It has practical value commendably and research signification to the designing of the best incentive contract. Key Words: Change point Geometric distributed lag model Stock index futures Principal-agent model Schwarz info
15、rmation criterion Koyck transformation Hedging Kuhn - Tucher conditions III 独创性声明 本人声明所呈交的学位论文是我个人在导师指导下进行的研宄工作及取得的研 宄成果。尽我所知,除文中已经标明引用的内容外,本论文不包含任何其他个人或 集体已经发表或撰写过的研宄成果。对本文的研宄做出贡献的个人和集体,均已在 文中以明确方式标明。本人完全意识到,本声明的法律结果由本人承担。 学位论文作 者签名: 日期: 年月 日 学位论文版权使用授权书 本学位论文作者完全了解学校有关保留、使用学位论文的规定,即:学校有权 保留并向国家有关部
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- 转变 经济 金融 计量 经济学 中的 数学 建模 结构性 变化 研究 及其 应用 沈卉卉
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