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  本文關鍵詞：在Knight不確定和部分信息下最優(yōu)消費投資問題研究　出處：《安徽工程大學》2013年碩士論文　論文類型：學位論文

  更多相關文章： 部分信息 奈特不確定 均值回復利率 隱馬爾科夫濾波模型 Malliavin分析 α-最大最小期望效用 最優(yōu)消費和投資組合

【摘要】：在金融數(shù)學領域中,最優(yōu)消費投資問題研究是最基本的內(nèi)容之一,已被國內(nèi)外眾多學者所研究.在現(xiàn)實的經(jīng)濟環(huán)境下,不僅要考慮部分信息對最優(yōu)消費投資決策的影響,還要考慮投資者對未來投資前景所持態(tài)度的不同而造成的最優(yōu)消費投資決策的差異.本文在奈特不確定和部分信息下,運用隨機最優(yōu)控制的方法,建立最優(yōu)消費投資模型.從而我們可以導出使得投資者消費和終端財富期望效用最大化的最優(yōu)交易策略.這些理論的建立可以很好地指導實際. 本文首先討論了在部分信息下股票支付紅利的最優(yōu)交易策略.考慮一個多種股票模型,股票價格過程滿足隨機微分方程,股票價格的瞬時收益率由有限狀態(tài)連續(xù)時間的馬爾科夫鏈刻畫.在投資者終端財富預期效用最大化目標下,利用隱馬爾科夫模型(HMM)濾波理論和Malliavin分析,導出最優(yōu)交易策略的顯式表達式.其次在上述內(nèi)容的基礎上研究了在奈特不確定框架下的最優(yōu)交易策略.文中刻畫了α-最大最小期望效用(α-MEU).該模型的主要特征是分離了含糊和含糊態(tài)度,其中含糊被刻畫為決策者的主觀信仰,而含糊態(tài)度被刻畫為決策者的含糊品味.在奈特不確定投資者a-最大最小期望效用最大化目標下,求解出最優(yōu)交易策略.最后研究了在均值回復利率下奈特不確定投資者的最優(yōu)消費投資策略.文中采用遞推多先驗效用,給出了α-MEU的表達式,導出了在冪效用下利率為均值回復過程的最優(yōu)投資組合. 通過上述問題的研究,使得我們的模型較傳統(tǒng)的Merton模型更加完善,更加符合實際,這對投資者在市場中選擇最優(yōu)消費投資策略具有一定的現(xiàn)實指導作用.
[Abstract]:In the field of financial mathematics, the study of optimal consumption and investment is one of the most basic contents, which has been studied by many scholars at home and abroad. We should not only consider the influence of some information on the optimal consumption and investment decision. Considering the difference of the optimal consumer investment decision caused by the different attitude of the investors to the future investment prospects, this paper uses the stochastic optimal control method under the Knight uncertainty and partial information. By establishing the optimal consumption and investment model, we can derive the optimal trading strategy that maximizes the expected utility of investors' consumption and terminal wealth. The establishment of these theories can well guide the practice. In this paper, we first discuss the optimal trading strategy of dividend payment under partial information. Considering a variety of stock models, the stock price process satisfies the stochastic differential equation. The instantaneous return rate of stock price is characterized by Markov chain of finite state continuous time, under the goal of maximizing expected utility of investor terminal wealth. The hidden Markov model (hmm) filtering theory and Malliavin analysis are used. The explicit expression of the optimal trading strategy is derived. Secondly, the optimal trading strategy under the framework of Knight uncertainty is studied on the basis of the above contents. The 偽 -maximum and minimum expected utility (偽 -MEUU) is characterized in this paper. The main feature of the model is the separation of ambiguity and ambiguity. Ambiguity is described as the subjective belief of the decision-maker, and the vague attitude is characterized as the vague taste of the decision-maker. In the case of Knight's uncertain investor a-maximum expected utility maximization goal. Finally, the optimal consumer investment strategy of Knight uncertain investors under the mean return interest rate is studied. In this paper, the expression of 偽 -MEU is given by using recursive multi-priori utility. The optimal portfolio with the interest rate as the mean return process is derived under the power utility. Through the study of the above problems, our model is more perfect than the traditional Merton model, more in line with the reality. This has a certain practical guiding role for investors to choose the optimal consumption and investment strategy in the market.
【學位授予單位】：安徽工程大學
【學位級別】：碩士
【學位授予年份】：2013
【分類號】：F830.59;F224

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本文編號：1391419