本文選題：穩(wěn)定分布 + 投資組合�。� 參考：《鄭州大學(xué)》2015年碩士論文

【摘要】：投資組合問(wèn)題作為現(xiàn)代金融學(xué)的一個(gè)核心課題,主要研究在不確定情況下對(duì)資產(chǎn)進(jìn)行最優(yōu)配置與選擇,從而實(shí)現(xiàn)收益率最大化與風(fēng)險(xiǎn)最小化間的均衡。1952年,美國(guó)經(jīng)濟(jì)學(xué)家Markowitz[1]首次用資產(chǎn)收益率的方差度量風(fēng)險(xiǎn),并提出了均值-方差投資組合模型,被認(rèn)為開創(chuàng)了現(xiàn)代投資組合理論的先河,奠定了定量研究金融投資問(wèn)題的基礎(chǔ)。但是,Markowitz的均值-方差投資組合模型必須依賴于資產(chǎn)的收益率服從正態(tài)分布且方差存在,而大量的實(shí)證研究證明,無(wú)論是收益率的正態(tài)假設(shè)還是方差的存在性都是值得懷疑的�；贛arkowitz理論框架下的投資組合模型,對(duì)輸入的參數(shù)要求嚴(yán)格,但是,對(duì)未來(lái)資產(chǎn)的回報(bào)做精準(zhǔn)的預(yù)測(cè)非常困難,并且在不同的經(jīng)濟(jì)環(huán)境中,各資產(chǎn)之間的相關(guān)性是變化的,很難預(yù)測(cè)未來(lái)資產(chǎn)之間的相關(guān)性。針對(duì)上述問(wèn)題,本文運(yùn)用不同的風(fēng)險(xiǎn)度量并引入具有尖峰厚尾特征的穩(wěn)定分布來(lái)研究投資組合理論。穩(wěn)定分布具有四個(gè)參數(shù),但是沒(méi)有解析的密度函數(shù)和分布函數(shù)的表達(dá)式,為此文章研究高效快速的數(shù)值算法來(lái)解決穩(wěn)定分布給模型帶來(lái)的計(jì)算量和復(fù)雜性。文章通過(guò)實(shí)證研究部分,對(duì)各個(gè)模型進(jìn)行對(duì)比分析,發(fā)現(xiàn)基于穩(wěn)定分布的均值-絕對(duì)離差模型和均值-半絕對(duì)離差模型與正態(tài)分布下對(duì)應(yīng)的模型相比,有效前沿向左上方移動(dòng),且計(jì)算出的最優(yōu)比例的投資效果更佳。本文介紹了風(fēng)險(xiǎn)平價(jià)理論,并對(duì)該理論下的模型進(jìn)行修正改進(jìn),求出模型的最優(yōu)比例。
[Abstract]:As a core subject of modern finance, portfolio problem is mainly concerned with the optimal allocation and selection of assets under uncertain conditions, so as to achieve the equilibrium between maximization of return rate and minimization of risk. The American economist Markowitz [1] measures the risk with the variance of the return on assets for the first time, and puts forward the mean-variance portfolio model, which is regarded as the pioneer of the modern portfolio theory and lays the foundation for the quantitative study of the financial investment problem. However, Markowitz's mean-variance portfolio model must depend on the return of assets from the normal distribution and the existence of variance, and a large number of empirical studies prove that the existence of both the normal assumption of return and variance is doubtful. The portfolio model based on Markowitz theory requires strict input parameters, but it is very difficult to predict the return of future assets accurately, and the correlation between assets varies in different economic environments. It is difficult to predict the correlation between future assets. In order to solve the above problems, this paper uses different risk measures and introduces a stable distribution with peak and thick tail to study portfolio theory. The stable distribution has four parameters, but there is no analytic density function and distribution function expression. In this paper, an efficient and fast numerical algorithm is studied to solve the computational complexity and complexity brought by the stable distribution to the model. In the part of empirical research, we find that the mean-absolute deviation model and the mean-semi-absolute deviation model based on stable distribution move to the upper left of the model compared with the corresponding model under normal distribution. And the optimal proportion of the calculated investment effect is better. In this paper, the theory of risk parity is introduced, and the model under the theory is modified and improved to find the optimal proportion of the model.
【學(xué)位授予單位】：鄭州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：F830.59;F224

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