本文關(guān)鍵詞：期望效用最大化下的投資組合模型研究　出處：《廣西大學》2014年碩士論文　論文類型：學位論文

  更多相關(guān)文章： 期望效用 最優(yōu)決策 泰勒展開 動態(tài)投資組合 價值函數(shù) HJB方程

【摘要】：投資組合模型的構(gòu)建不僅對投資者的最優(yōu)投資決策起到至關(guān)重要的指導作用,也是金融經(jīng)濟學,特別是資產(chǎn)定價研究領(lǐng)域的重要問題之一.現(xiàn)實資本市場中存在著許多隨機不確定因素,面對這些不確定問題最有效的研究方法就是期望效用理論.期望效用理論認為投資者在投資過程中所追求的并不是最終能夠獲得的財富水平,而是最終能夠獲得的期望效用.本文主要基于期望效用最大化的目標來建立投資組合模型,主要研究內(nèi)容和成果如下： (1)當效用函數(shù)是CARA型效用函數(shù)時,通過對期望財富效用函數(shù)的泰勒展開,得到了高階矩風險與期望財富效用的關(guān)系：偏度與期望財富效用是正相關(guān)的；峰度與期望財富效用是負相關(guān)的,以及當效用函數(shù)是二次函數(shù)且收益服從正態(tài)分布時均值-方差模型與期望效用模型等價.隨后,文中建立了CARA型效用函數(shù)靜態(tài)模型并給出簡化的隱式解. (2)面對非隨機的不確定因素時,模糊理論比期望效用理論更加合理.文中用可能性均值和可能性方差度量投資組合的收益和風險,構(gòu)建了帶有流動性的模糊投資組合模型,用Lagrange乘子法求出其最優(yōu)解,并給出數(shù)值結(jié)果. (3)基于投資者投資周期內(nèi)累積的期望效用最大化的目標,文中在三種不同的假設(shè)環(huán)境中分別建立了對應(yīng)的動態(tài)投資組合模型.從三個模型的最優(yōu)決策中可以得到以下規(guī)律：最優(yōu)投資比例不受投資者財富水平、消費水平和非資本收入水平的影響；最優(yōu)消費水平取決于投資者的財富水平.
[Abstract]:The construction of portfolio model not only plays an important role in guiding investors' optimal investment decision, but also plays an important role in financial economics. In particular, one of the most important problems in the field of asset pricing is the existence of many random uncertainties in the real capital market. In the face of these uncertainties, the most effective research method is expected utility theory, which holds that what investors are pursuing in the process of investment is not the level of wealth that can be obtained in the end. This paper is based on the goal of maximizing expected utility to establish a portfolio model, the main research content and results are as follows: 1) when utility function is CARA type utility function, Taylor expansion of expected wealth utility function is adopted. The relationship between higher moment risk and expected wealth utility is obtained: bias is positively related to expected wealth utility; The kurtosis is negatively correlated with the expected wealth utility, and the mean-variance model is equivalent to the expected utility model when the utility function is a quadratic function and the income is from the normal distribution. In this paper, the static model of utility function of CARA type is established and the simplified implicit solution is given. In the face of non-random uncertainty, fuzzy theory is more reasonable than expected utility theory. In this paper, the probability mean and possibility variance are used to measure the return and risk of the investment portfolio. A fuzzy portfolio model with liquidity is constructed. The optimal solution is obtained by Lagrange multiplier method and the numerical results are given. Based on the objective of maximizing the expected utility accumulated in the investor's investment cycle. In this paper, the corresponding dynamic portfolio models are established in three different hypothetical environments. From the optimal decision of the three models, the following laws can be obtained: the optimal investment ratio is not subject to the wealth level of the investors. The influence of consumption level and non-capital income level; The optimal level of consumption depends on the level of wealth of investors.
【學位授予單位】：廣西大學
【學位級別】：碩士
【學位授予年份】：2014
【分類號】：F830.59;O225

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