本文選題：投資組合優(yōu)化 + 人工蜂群算法�。� 參考：《西安電子科技大學》2012年博士論文

【摘要】：投資組合優(yōu)化問題作為現(xiàn)代金融學的一個核心課題，主要研究如何在不確定情況下對金融資產(chǎn)進行合理配置與選擇，從而實現(xiàn)收益率最大化與風險最小化間的均衡．1952年，美國經(jīng)濟學家HarryM.Markowitz在《TheJournalofFinance》雜志上發(fā)表了“PortfolioSelection”一文，首次使用證券收益方差度量風險，提出了均值-方差投資組合選擇理論，被學術界公認為開創(chuàng)了現(xiàn)代投資組合理論的先河，奠定了定量化研究金融投資問題的基礎．隨著現(xiàn)代數(shù)學方法的發(fā)展及應用數(shù)學方法研究金融經(jīng)濟問題的金融數(shù)學的問世，使得現(xiàn)代金融投資理論開始擺脫純粹經(jīng)驗化操作和單純描述性研究的狀態(tài)，進入了定量分析這一高級階段，并為投資者進行投資決策提供了指導．當今世界經(jīng)濟飛速發(fā)展，金融危機和市場波動頻繁出現(xiàn)，我國的資本市場雖然在改革開放之后得到長足發(fā)展，但還不太完善和成熟，使得投資者面臨越來越多錯綜復雜的金融投資決策的理論和實踐問題，對投資組合優(yōu)化問題的研究也越來越具有重要的理論和現(xiàn)實意義． 本文從以下三個方面開展研究工作，，一是帶有基數(shù)約束的投資組合優(yōu)化問題，二是帶有交易費用的動態(tài)投資組合優(yōu)化問題，三是投資組合隨機優(yōu)化模型的情景生產(chǎn)方法比較．主要工作如下： 1.人工蜂群算法是近幾年提出的一種新的群智能算法，在求解多峰高維函數(shù)優(yōu)化問題時體現(xiàn)出了更為優(yōu)良的性質(zhì)．考慮到人工蜂群算法的這一優(yōu)點，利用人工蜂群算法研究了帶有基數(shù)約束的投資組合優(yōu)化模型．通過數(shù)值試驗可以發(fā)現(xiàn)，人工蜂群算法在求解這一問題時，比別的智能優(yōu)化算法體現(xiàn)出一些更優(yōu)越的性態(tài)． 2.針對帶有基數(shù)約束的投資組合優(yōu)化問題，提出一種改進人工蜂群算法．在算法中，利用Deb選擇策略使最優(yōu)解滿足約束條件，并引入新的搜索策略以提高算法的收斂速度；同時，使用Bolzmann選擇概率來維護種群多樣性，防止算法早熟．通過對測試問題的數(shù)值實驗，表明使用該算法能獲得更好的投資策略，有效分散投資組合風險，并說明該算法對于求解投資組合優(yōu)化問題是快速有效的． 3.研究了存在固定交易費用和比例交易費用情況下的多階段均值-方差投資組合優(yōu)化問題．應用離散時間動態(tài)規(guī)劃方法，給出了投資者的間接效用函數(shù)、無交易區(qū)域邊界和有效前沿的解析解，從而確定了投資者的長期最優(yōu)投資策略．通過數(shù)值試驗描述了問題的求解過程，并說明了交易費用對有效前沿的影響． 4.研究了連續(xù)時間情形下，帶有固定交易費用和比例交易費用的均值-方差投資組合優(yōu)化問題．通過使用動態(tài)規(guī)劃方法，推導出了原問題的Hamilton-Jacobi-Bellman方程，并得到了方程的顯式解．從而，推導出原均值-方差問題的最優(yōu)投資策略和有效前沿的表達式．數(shù)值試驗給出了交易費用的變化對交易區(qū)域和有效前沿的影響，并說明了所給方法的可行性和有效性． 5.比較研究了四種情景生成方法在求解投資組合優(yōu)化問題時的預測與決策效果．通過對比其樣本內(nèi)性質(zhì)及樣本外性質(zhì)發(fā)現(xiàn)，情景生成方法與投資組合優(yōu)化模型對于中國股票市場來說，在預測與決策方面是非常有效的工具．其中矩匹配方法較其他方法能更好的反映市場的下跌趨勢，多變量GARCH方法能更好的反映市場的上漲趨勢． 最后，列出了投資組合優(yōu)化問題研究中有待進一步研究的幾個問題．
[Abstract]:As a core subject of modern finance , the optimization problem of portfolio optimization focuses on how to make rational allocation and selection of financial assets under uncertain circumstances , so as to realize the equilibrium between yield maximization and risk minimization . In 1952 , U.S . economist HarryM . markwitz published " PortfolioSelection " in the journal of Finance Journal , and proposed the mean - variance portfolio selection theory . With the development of modern mathematics method and the application of mathematical method to study the financial mathematics of financial economy , the modern financial investment theory begins to get rid of the state of purely empirical operation and simple descriptive study . It has entered the advanced stage of quantitative analysis and provides guidance for investors to make investment decision . The rapid development of the world economy , the financial crisis and the frequent fluctuation of the market , the capital market of our country has been developed after the reform and opening up , but it is not too perfect and mature , so that the investors face more and more complex financial investment decision - making theories and practical problems , and the research on the optimization of investment portfolio is more and more important theoretical and practical significance .

This paper carries out the research work from the following three aspects : one is the optimization problem of portfolio optimization with base constraint , the second is the dynamic portfolio optimization problem with transaction cost , and the third is the comparison of the scenario production method of the investment portfolio stochastic optimization model . The main work is as follows :

1 . Artificial Bee Colony Algorithm is a new swarm intelligence algorithm proposed in recent years , which is more excellent in solving the problem of multi - modal high - dimensional function optimization . Considering the advantage of artificial swarm algorithm , an optimization model of portfolio optimization with radix constraint is studied by means of artificial swarm algorithm . Through numerical experiments , it can be found that the artificial swarm optimization algorithm is superior to other intelligent optimization algorithms when solving this problem .

2 . Aiming at the optimization problem of portfolio optimization with radix constraint , an improved artificial swarm optimization algorithm is proposed . In the algorithm , the Deb selection strategy is used to make the optimal solution satisfy the constraint condition , and a new search strategy is introduced to improve the convergence speed of the algorithm ;
At the same time , the bolzmann selection probabilities are used to maintain the population diversity and prevent the early maturity of the algorithm . Through the numerical experiments on the test problem , it is shown that using the algorithm can obtain better investment strategy and effectively disperse the portfolio risk , and show that the algorithm is fast and effective for solving the problem of portfolio optimization .

3 . A multi - stage mean - variance portfolio optimization problem with fixed transaction costs and proportional transaction costs is studied . Using the discrete - time dynamic programming method , the indirect utility function , the non - transaction region boundary and the analytic solution of the effective frontier are given , and the long - term optimal investment strategy of investors is determined . The solution process of the problem is described by numerical tests , and the influence of transaction cost on the effective frontier is explained .

4 . The optimal problem of mean - variance portfolio optimization with fixed transaction cost and proportional transaction cost is studied under the continuous time situation . By using the dynamic programming method , the Hamilton - BI - Bellman equation of the original problem is derived , and the explicit solution of the equation is obtained . Therefore , the optimal investment strategy and effective frontier expression of the original mean - variance problem are derived . The numerical test gives the effect of the change of transaction cost on the transaction area and effective frontier , and illustrates the feasibility and effectiveness of the method .

5 . The forecasting and decision - making effect of four scenarios generation method in solving the problem of portfolio optimization is studied . By comparing the intra - sample properties and the out - of - sample properties , the scenario - generating method and portfolio optimization model are very effective in forecasting and decision - making for Chinese stock market . Among them , the moment matching method can better reflect the market ' s declining trend compared with other methods , and the multi - variable forecasting method can better reflect the rising trend of the market .

Finally , several problems to be studied in the research of portfolio optimization are listed .
【學位授予單位】：西安電子科技大學
【學位級別】：博士
【學位授予年份】：2012
【分類號】：F224;F830.59

【引證文獻】

相關期刊論文 前1條

1 何紅;拓守恒;;利用和聲搜索算法求解投資組合最優(yōu)化研究[J];商業(yè)研究;2014年04期

相關碩士學位論文 前1條

1 付海東;投資組合風險測度研究[D];蘭州大學;2013年

本文編號：2039225