發(fā)布時間：2018-01-29 16:35

  本文關(guān)鍵詞： 人工魚群 投資組合 均勻變異 Levy變異 優(yōu)化求解　出處：《天津商業(yè)大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：隨著經(jīng)濟的飛速發(fā)展,證券投資市場猶如雨后春筍般不斷生長,大量的企業(yè)和個人對各種證券商品進行投資買賣。在證券市場中,投資本身就會帶有一定的風(fēng)險,有些資產(chǎn)具有高風(fēng)險,而有些資產(chǎn)具有低風(fēng)險,投資者必須選擇購買哪些證券產(chǎn)品,使得收益更高,這對不同的投資者來說,顯得尤為重要。有的投資者具有冒險精神,希望通過高風(fēng)險的手段獲取較高的收益;另外一些不愿意承受如此大的風(fēng)險,他們更喜歡低風(fēng)險的投資方式。如何合理選擇投資方案,使投資者在可接受的風(fēng)險范圍內(nèi)獲取最高收益,成為目前眾多學(xué)者研究的熱點。自Markowitz首次提出以均值-方差為基礎(chǔ)的投資組合問題模型后,許多學(xué)者開始采用各種算法對投資組合模型進行優(yōu)化求解。人工魚群算法作為一種新興的優(yōu)化算法,具有簡單、高效和靈活等特點,目前得到廣泛應(yīng)用。但也存在收斂精度不高、易陷入局部極值以及優(yōu)化求解不夠穩(wěn)定等不足。因此,本文首先對魚群算法進行改進,然后用于考慮交易費用的投資組合模型的優(yōu)化求解,獲得較好效果。主要工作包括:(1)針對人工魚群算法的不足,研究了兩種改進方式,一種是利用均勻分布產(chǎn)生均勻分布算子,并與基本魚群算法相結(jié)合,當連續(xù)若干次收斂最優(yōu)值變化方差在允許誤差之內(nèi)時發(fā)生均勻變異,這樣能夠保證魚群跳出局部極值的陷阱,從而獲得全局最優(yōu)狀態(tài)。另一種是采用服從Levy分布的概率函數(shù)使魚群產(chǎn)生Levy變異,在尋優(yōu)過程中能夠跳出局部極值。經(jīng)測試函數(shù)仿真表明,改進算法提高了收斂精度和全局搜索能力、以及求解問題的穩(wěn)定性。同時對這兩種改進算法還采用自適應(yīng)視野和步長,進一步提高了算法的收斂性能。(2)在對一般投資組合模型研究的基礎(chǔ)上,引入交易費用,討論了考慮交易費用的投資組合模型。并以上海證券交易所五只股票100天的股票價格數(shù)據(jù)為實例,分別采用基本魚群算法、基于自適應(yīng)視野與步長均勻變異魚群算法和基于自適應(yīng)Levy變異人工魚群算法對投資組合模型進行優(yōu)化求解。結(jié)果表明,改進魚群算法可以獲得較好的投資效益,投資期望收益明顯提高、風(fēng)險降低。
[Abstract]:With the rapid development of economy, the securities investment market is growing like bamboo shoots after a spring rain. A large number of enterprises and individuals invest in various securities commodities. Investment itself will have a certain risk, some assets have high risk, while some assets have low risk, investors must choose which securities products to buy to make the return higher, this is for different investors. Some investors have the spirit of taking risks and hope to obtain higher returns by means of high risk; Others are not willing to take such a large risk, they prefer low-risk investment. How to choose a reasonable investment plan, so that investors can get the highest return within the acceptable risk range. Since Markowitz first proposed a portfolio problem model based on mean-variance. Many scholars began to use a variety of algorithms to optimize the portfolio model. Artificial fish swarm algorithm as a new optimization algorithm, with the characteristics of simple, efficient and flexible. At present, it is widely used. However, it also has some shortcomings such as low convergence precision, easy to fall into local extremum and unstable optimization. Therefore, this paper first improves the fish swarm algorithm. Then the optimal solution of portfolio model considering transaction cost is used to obtain better results. The main work includes: 1) aiming at the shortcomings of artificial fish swarm algorithm, two improved methods are studied. One is to use uniform distribution to generate uniform distribution operator, and combine with the basic fish swarm algorithm, when the variance of the optimal value of convergence is within the allowable error, the uniform variation occurs. In this way, the fish group can escape from the trap of local extremum and obtain the global optimal state. The other is to use the probability function of Levy distribution to make the fish herd produce Levy variation. It can jump out of the local extremum in the process of optimization. The test function simulation shows that the improved algorithm improves the convergence accuracy and global search ability. And the stability of solving the problem. At the same time, the adaptive field of vision and step size are also used to improve the convergence performance of the algorithm. 2) on the basis of the general portfolio model research. This paper introduces the transaction cost and discusses the portfolio model considering the transaction cost. Taking the 100-day stock price data of five stocks on the Shanghai Stock Exchange as an example, the basic fish swarm algorithm is adopted respectively. Based on adaptive visual field and step size uniform mutation fish swarm algorithm and adaptive Levy mutation artificial fish swarm algorithm to optimize the solution of the portfolio model. The improved fish swarm algorithm can obtain better investment benefit, the expected return of investment is obviously increased, and the risk is reduced.
【學(xué)位授予單位】：天津商業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224;F832.51

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