本文關(guān)鍵詞：基于股票配對策略的動(dòng)態(tài)資產(chǎn)配置研究　出處：《上海師范大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 配對交易 最優(yōu)策略 HJB方程 O-U過程 廣義網(wǎng)格

【摘要】：配對交易最早是由華爾街交易員Jesse Livermore創(chuàng)造的交易策略.隨著計(jì)算機(jī)技術(shù)的飛速發(fā)展,配對交易越來越廣泛地被運(yùn)用于金融市場中.2010年3月起我國證券市場相繼開展了融資融券業(yè)務(wù)和股指期貨業(yè)務(wù),這為配對交易策略在我國證券市場中的實(shí)現(xiàn)提供了前提與基礎(chǔ).目前關(guān)于配對交易的研究主要有兩類,一類是基于統(tǒng)計(jì)和數(shù)據(jù)挖掘方法實(shí)現(xiàn)配對交易,另一類則是基于方程方法實(shí)現(xiàn)配對交易.其中第一類的研究在應(yīng)用層面更為廣泛,但這一類的主要缺陷是無法通過配對標(biāo)的的頭寸數(shù)量來控制風(fēng)險(xiǎn).所以本文研究了在配對價(jià)差滿足O-U過程的條件下最優(yōu)投資策略問題.與先前一些學(xué)者的研究內(nèi)容不同,本文考慮了止損止盈策略.在第三章中,我們建立了最優(yōu)投資策略所滿足的HJB方程并在此基礎(chǔ)之上給出了止損或止盈時(shí)方程的邊界條件.但由此所建立的HJB方程很難求出解析解,因此我們運(yùn)用了有限差分法求解.為了保證系數(shù)矩陣的半正定性,我們使用了廣義網(wǎng)格的方法建立HJB方程的差分格式,將HJB方程近似為一個(gè)非線性方程組.之后,我們運(yùn)用迭代法和預(yù)處理共軛梯度法(PCG)求解該方程組從而得出HJB方程的數(shù)值解.然后我們針對不同的參數(shù)情況對最優(yōu)策略進(jìn)行了數(shù)值分析.在第四章中,為了確保第三章中差分格式以及迭代算法的正確性,我們研究了差分格式的相容性,單調(diào)性,穩(wěn)定性以及迭代算法的收斂性.在第五章中,我們進(jìn)一步拓展了基于配對交易的最優(yōu)策略模型.我們使用均值方差模型作為投資者的目標(biāo),同樣考慮止損止盈策略,然后建立HJB方程并運(yùn)用第三章中的方法求出了該方程的數(shù)值解.最后,我們進(jìn)行了數(shù)值分析,在其他參數(shù)條件不變的情況下比較了第三章的最優(yōu)策略與第五章中最優(yōu)策略的差異性.
[Abstract]:Pairing was first created by Jesse Livermore, a Wall Street trader, with the rapid development of computer technology. Pairing transactions are more and more widely used in the financial market. Since March 2010, China's securities market has carried out margin trading and stock index futures business one after another. This provides the premise and foundation for the realization of pairing trading strategy in Chinese securities market. At present, there are two kinds of research on pairing transaction, one is based on statistics and data mining method to realize pairing transaction. The other is the equation-based method to achieve pairing transactions, the first kind of research is more widely used in the field of application. However, the main defect of this kind is that the risk can not be controlled by the number of positions of the matched target. Therefore, this paper studies the optimal investment strategy under the condition that the pairing spread satisfies the O-U process. The content is different. This paper considers the stop loss and stop gain strategy in Chapter 3. We establish the HJB equation satisfied by the optimal investment strategy and give the boundary conditions of the stop loss or stop gain equation on this basis. However, the HJB equation is difficult to find the analytical solution. In order to guarantee the positive semidefinite of the coefficient matrix, we use the generalized grid method to establish the difference scheme of HJB equation. The HJB equation is approximated as a nonlinear system of equations. We use the iterative method and the preconditioned conjugate gradient method (PCG). The numerical solution of the HJB equation is obtained by solving the equations. Then we give a numerical analysis of the optimal strategy for different parameters. In Chapter 4th. In order to ensure the correctness of the difference scheme and the iterative algorithm in Chapter 3, we study the consistency, monotonicity, stability and convergence of the iterative algorithm. In Chapter 5th, we study the consistency, monotonicity, stability and convergence of the iterative algorithm. We further extend the optimal strategy model based on paired trading. We use the mean variance model as the target of investors and consider the stop loss and stop earnings strategy. Then the HJB equation is established and the numerical solution of the equation is obtained by using the method in Chapter 3. Finally, we carry out the numerical analysis. The differences between the optimal strategy in Chapter 3 and the optimal Policy in Chapter 5th are compared under the condition that other parameters are invariant.
【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F832.51;F224

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 蔡燕;王林;許莉莉;;基于隨機(jī)價(jià)差法的配對交易研究[J];金融理論與實(shí)踐;2012年08期

相關(guān)碩士學(xué)位論文 前2條

1 陳垣橋;配對交易策略的最佳信號機(jī)制研究[D];南京大學(xué);2015年

2 吳偉;基于神經(jīng)網(wǎng)絡(luò)模型的期貨合約套利策略研究[D];浙江財(cái)經(jīng)大學(xué);2015年

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本文編號：1407112