本文選題：模糊數(shù)　切入點(diǎn)：跟蹤誤差　出處：《湖南大學(xué)》2013年碩士論文　論文類(lèi)型：學(xué)位論文

【摘要】：在現(xiàn)代金融學(xué)里，基于隨機(jī)不確定性對(duì)投資組合選擇問(wèn)題的理論研究已經(jīng)發(fā)展到相當(dāng)成熟的地步，然而證券市場(chǎng)中的不確定性大多表現(xiàn)為模糊不確定性，而證券市場(chǎng)的模糊性在以往的理論研究中往往被忽略，因此，基于模糊不確定性對(duì)投資組合選擇問(wèn)題的研究在理論和實(shí)踐中都將具有非常重要和深遠(yuǎn)的意義。 本文將模糊數(shù)理論與指數(shù)化投資理論相結(jié)合，在摩擦市場(chǎng)下，，構(gòu)建了三種基于增強(qiáng)型跟蹤指數(shù)模型的模糊投資組合選擇模型。本文的模型對(duì)于金融市場(chǎng)中的摩擦因素只考慮了與交易數(shù)量成比例的交易費(fèi)用。本文采用極大極小半絕對(duì)偏差跟蹤指數(shù)誤差來(lái)度量風(fēng)險(xiǎn)，并使它達(dá)到最小化得到跟蹤指數(shù)投資組合模型�？紤]到現(xiàn)實(shí)市場(chǎng)中的賣(mài)空限制、交易費(fèi)用以及投資者對(duì)于投資組合期望收益的約束條件，即投資者對(duì)投資組合的收益有個(gè)最低的收益要求，從而得到增強(qiáng)型跟蹤指數(shù)模型。本文首先把流動(dòng)性引進(jìn)來(lái)，把投資組合的流動(dòng)性看作模糊數(shù)，于是得到第一個(gè)模型—帶有模糊流動(dòng)性約束的增強(qiáng)型跟蹤指數(shù)投資組合模型。由于投資者對(duì)投資組合期望收益的滿(mǎn)意水平以及跟蹤誤差的承受水平是不確定和模糊的，因此，我們把這些目標(biāo)水平看作半梯形模糊隸屬函數(shù)，以此來(lái)衡量投資者的滿(mǎn)意程度，于是構(gòu)建了基于模糊決策的增強(qiáng)型跟蹤指數(shù)投資組合選擇模型。接著，本文在考慮到投資者對(duì)跟蹤指數(shù)誤差、投資組合期望收益和流動(dòng)性這三個(gè)目標(biāo)的情況下，用對(duì)數(shù)型隸屬函數(shù)分別來(lái)描述投資者對(duì)這三個(gè)目標(biāo)的滿(mǎn)意程度，繼而構(gòu)建了多目標(biāo)的模糊增強(qiáng)型跟蹤指數(shù)模型。 最后，本文選取滬深300指數(shù)作為跟蹤標(biāo)的指數(shù)，選取滬深300指數(shù)成份股作為投資目標(biāo)進(jìn)行實(shí)證分析，通過(guò)變化隸屬函數(shù)的參數(shù)值來(lái)盡可能準(zhǔn)確地描述投資者對(duì)目標(biāo)水平的滿(mǎn)意程度，最后得到不同參數(shù)下投資者的投資組合。
[Abstract]:In modern finance, the theoretical research on portfolio selection based on stochastic uncertainty has developed to a rather mature stage, but the uncertainty in the securities market is mostly fuzzy uncertainty. However, the fuzziness of the securities market is often ignored in the previous theoretical studies. Therefore, the study of portfolio selection based on fuzzy uncertainty will be of great significance in both theory and practice. In this paper, the fuzzy number theory and the indexed investment theory are combined in the friction market. Three fuzzy portfolio selection models based on the enhanced tracking index model are constructed. In this paper, only the transaction costs proportional to the number of transactions are considered for the friction factors in the financial market. Small absolute deviations track exponential errors to measure risk, Considering the short selling restrictions, transaction costs and the constraints of investors on the expected return of the portfolio, the model is minimized to obtain the tracking index portfolio model. That is, the investors have a minimum return requirement on the return of the investment portfolio, thus an enhanced tracking index model is obtained. In this paper, the liquidity of the portfolio is first introduced, and the liquidity of the portfolio is regarded as a fuzzy number. The first model, an enhanced tracking index portfolio model with fuzzy liquidity constraints, is obtained. Since the investors' satisfaction with the expected return of the portfolio and the tolerance level of the tracking error are uncertain and fuzzy, We regard these target levels as semi-trapezoidal fuzzy membership functions to measure investor satisfaction, so we construct an enhanced tracking index portfolio selection model based on fuzzy decision. In this paper, the logarithmic membership function is used to describe the degree of satisfaction of investors with the three objectives of tracking the index error, the expected return of the investment portfolio and the liquidity, and the logarithmic membership function is used to describe the degree of satisfaction of the three objectives. Then the fuzzy enhanced tracking index model of multi-targets is constructed. Finally, this paper selects the Shanghai and Shenzhen 300 index as the tracking target index, and selects the Shanghai and Shenzhen 300 index component stock as the investment target to carry on the empirical analysis. By changing the parameter value of the membership function, the degree of satisfaction of the investor to the target level is described as accurately as possible. Finally, the portfolio of the investor under different parameters is obtained.
【學(xué)位授予單位】：湖南大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2013
【分類(lèi)號(hào)】：F830.91;F224

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