本文關鍵詞：時變金融市場下動態(tài)投資組合選擇理論及其應用研究　出處：《湖南大學》2016年博士論文　論文類型：學位論文

  更多相關文章： 動態(tài)投資組合選擇 隨機投資機會集 隨機微分博弈 納什均衡 跨期對沖需求

【摘要】：金融市場中充滿了各種不確定性和時變性,投資者在投資中必然面臨風險。怎樣有效地控制和管理風險,如何通過分散化金融投資形成最優(yōu)投資組合,有效地降低投資者面臨的非系統(tǒng)性風險,就成為了投資者必須面對的一大挑戰(zhàn)和難題。在現(xiàn)實中,不同的投資可能會產(chǎn)生不同的風險。特別的,短期投資者與長期投資者的最優(yōu)投資需求是完全不一樣的。通常短期投資者只關心在一個時期內的資產(chǎn)(組合)收益率的均值與風險,而忽略了投資機會集在下一個時期的可能變化,短期投資者的投資行為在這種情形下被認為是短視的。傳統(tǒng)的資產(chǎn)組合選擇理論忽略了投資機會集的變化和金融市場資產(chǎn)價格的時變特征對投資決策的影響。金融市場中大量的時變經(jīng)驗事實特征,比如,協(xié)整效應、動量效應、隨機利率、隨機波動率以及宏觀經(jīng)濟狀態(tài)隨機轉換都表明投資機會集不是固定不變的,而是具有隨機性特征。實踐中,投資者的投資行為通常是動態(tài)多期的,他們不只是關心當期投資機會集對于財富的沖擊,而且關心投資機會集未來的隨機性對于財富的跨期沖擊。由于投資機會集隨時間變化,投資者除了對金融資產(chǎn)的短視需求外,還具有跨期對沖需求,即利用金融資產(chǎn)來規(guī)避隨機投資機會集的跨期沖擊。因此,從長期視角出發(fā),基于金融市場的多個時變特征,對動態(tài)投資組合選擇問題的研究不僅具有重大的理論價值,也具有重要的現(xiàn)實意義。在這種背景下,本論文研究了基于多個不同金融市場特征下動態(tài)投資組合選擇的若干問題,綜合運用效用函數(shù)理論、隨機控制理論和隨機微分博弈理論,建立嚴格的數(shù)理金融模型,系統(tǒng)的探討了模型特征、適用條件、投資與消費行為、跨期對沖需求、配對交易和動量投資策略等規(guī)律。主要研究成果簡述如下:首先,針對股票價格之間的協(xié)整效應時變特征,研究了金融市場的股票資產(chǎn)存在協(xié)整關系的,投資者該如何進行投資與消費�；趨f(xié)整資產(chǎn)價格模型,以有限期消費總效用和終端時刻財富期望效用的最大化為決策目標,分別在冪效用和對數(shù)效用函數(shù)下,推導出了最優(yōu)化問題價值函數(shù)的高維、非線性、非齊次的Hamilton-Jacobi-Bellman(HJB)方程。給出了最優(yōu)投資、最優(yōu)消費的顯式的表達式。討論了動態(tài)優(yōu)化模型的四種特殊情形:投資者只關心終端時刻的財富效用最大化;投資者只關心有限期的消費總效用最大化;股票價格之間不存在協(xié)整關系以及風險厭惡系數(shù)為零。在理論分析的基礎上,分析了協(xié)整效應對于投資者的福利,最優(yōu)投資與最優(yōu)消費的影響。結果表明,當兩個風險資產(chǎn)的價格都被低估時,投資者通過借貸買入兩個風險資產(chǎn)。當兩個風險資產(chǎn)的價格都被高估時,具有較高風險厭惡程度的投資者賣空全部的風險資產(chǎn)。當其中一個資產(chǎn)的價格被高估,另一個資產(chǎn)的價格被低估時,發(fā)現(xiàn)投資者在金融市場中采取一種“多頭-空頭”投資模式,這為實踐中配對交易策略提供了理論支持。其次,針對股票收益在短時期內具有動量效應時變特征,研究了股票收益存在動量效應的最優(yōu)投資和消費問題�；趧恿啃獌r格模型,以整個生命期的消費效用最大化為決策目標。在單位跨期替代彈性系數(shù)下,推導出了價值函數(shù)、最優(yōu)投資和最優(yōu)消費的精確顯式表達式;在跨期替代彈性系數(shù)不為1時,通過對數(shù)線性化方法,推導出了價值函數(shù)、最優(yōu)投資和最優(yōu)消費的近似解析表達式。在此基礎上,利用中國股票市場數(shù)據(jù)對模型的參數(shù)進行了校準,分析了動量效應對于最優(yōu)投資與最優(yōu)消費行為模式的影響。研究結果表明,個人偏好參數(shù)中,相對風險厭惡水平對于最優(yōu)投資策略的影響遠比跨期替代彈性系數(shù)重要;在動量狀態(tài)變量的初始值取溫和的負值時,最優(yōu)投資需求都大于零,跨期對沖需求小于零,并且當風險厭惡系數(shù)大于1時,跨期對沖需求在總的投資需求占有非常重要的權重;當動量狀態(tài)變量初始值為正或者溫和的負值時,跨期對沖需求為負,其極大的降低了股票上的投資;而當動量狀態(tài)變量初始值為深度的負值時,跨期對沖需求為正,將極大的增加在股票上的投資。個人偏好參數(shù)中,跨期替代彈性對于最優(yōu)消費財富比的影響遠比風險厭惡系數(shù)重要。進一步,給定風險厭惡系數(shù),最優(yōu)消費與財富之比是跨期替代彈性系數(shù)的單調減函數(shù);給定跨期替代彈性系數(shù),最優(yōu)消費與財富之比是風險厭惡系數(shù)的減函數(shù)。再次,考慮了兩個投資者面對同一投資機會集時最優(yōu)交互投資組合決策問題。利用常彈性方差隨機波動率模型來描述“波動率微笑”現(xiàn)象。以投資者終止時刻個人的財富以及與競爭對手財富的相對距離的加權平均的效用最大化為投資目標,通過隨機控制理論,推導出價值函數(shù)所滿足的一般hamilton-jacobi-bellman(hjb)方程。在指數(shù)效用和冪效用函數(shù)下,推導出了均衡策略的顯式表達式。在此基礎上,針對不同的模型參數(shù),對指數(shù)效用函數(shù)下的均衡策略進行了分析。結果發(fā)現(xiàn),均衡策略為投資期限、股票收益的波動率相關參數(shù)、彈性系數(shù)、投資者自身的風險厭惡系數(shù)以及無風險利率的單調遞減函數(shù);均衡策略為股票初始價格的增函數(shù),并且隨股票的期望收益率先增后減。最后,為了研究通貨膨脹和宏觀經(jīng)濟狀態(tài)的隨機轉換對于投資決策的影響,建立了馬爾可夫機制轉換資產(chǎn)價格模型,利用隨機微分博弈理論,考慮了兩個投資者面對相關但卻不同的投資機會集時最優(yōu)交互投資組合決策問題。以兩個投資者終止時刻財富和的效用最大化為投資目標,推導出了價值函數(shù)所滿足的一般hamilton-jacobi-bellman(hjb)方程。進一步,在冪效用帶通脹的模型下,推導出價值函數(shù)的feynman-kac表示和均衡策略的顯式表達式。在指數(shù)效用無通脹的模型下,也推導出價值函數(shù)feynman-kac表示和均衡策略的顯式表達式。在此基礎上,特別的討論了兩機制狀態(tài)轉換模型,針對不同的模型參數(shù),分析了機制轉換對于影響。結果顯示,宏觀經(jīng)濟狀態(tài)轉換對于最優(yōu)投資組合策略存在著顯著的影響。
[Abstract]:The financial market is full of uncertainty and variability, investors will face the risk in the investment. How to effectively control and manage the risk, how to form diversified financial investment portfolio, effectively reduce the non system risk faced by investors, it becomes a big challenge and problem in the real investors must face. In different investment may have different risk. In particular, the optimal investment demand for short-term investors and long-term investors are completely different. Usually short-term investors only care about in a period of assets (combination) and average risk return rate, while ignoring the investment opportunity set in may change next during the period, short-term investment behavior of investors in this case is considered to be short-sighted. The traditional portfolio selection theory ignores the investment opportunity set and the change of financial market Influence of asset price time-varying characteristics of investment decisions. In a large number of features, such as financial markets, cointegration effect, momentum effect, stochastic interest rate, stochastic volatility and macroeconomic state conversion shows that random investment opportunity set is not fixed, but with random characteristics. In practice, the behavior of investors is usually dynamic multi period, they not only care about the current investment opportunity set for the impact of wealth, but also with the investment opportunity set for the future stochastic intertemporal wealth shocks. As the investment opportunity set change with time, in addition to the investor demand for financial assets short-sighted, also has the intertemporal hedging demands that is, the use of the financial asset investment opportunity set to avoid random intertemporal shocks. Therefore, starting from the long-term perspective, characteristics of multiple financial markets based on the choice of dynamic portfolio The research not only has great theoretical value, but also has important practical significance. In this background, this paper studies the problems of dynamic portfolio choice of a number of different financial markets characteristics based on the integrated use of the utility theory, stochastic control theory and stochastic differential game theory, establish the model of mathematical finance strictly. The system discussed the characteristic of the model, the applicable conditions, the behavior of consumption and investment, hedging demand, investment strategy and momentum pair trading rules. The main research results are as follows: first of all, in between the stock price cointegration effect the time-varying characteristics of the stock assets of the financial market there is a cointegration relationship, investors how to carry on the investment and consumption. The cointegration model based on asset prices, to maximize the total utility of finite period consumption and terminal wealth utility for the moment decision objective, respectively. In the power utility and the logarithmic utility function, deduced the high dimensional nonlinear optimization problems, the value function, non homogeneous Hamilton-Jacobi-Bellman (HJB) equation is given. The optimal investment, the explicit solution of optimal consumption. Discussed four special cases: a dynamic optimization model to maximize investors only care about the terminal time the utility of wealth; the total utility of investors only care about the period of maximum consumption; the stock price does not exist between the cointegration relation and the risk aversion coefficient is zero. On the basis of theoretical analysis, analysis of the welfare effect of cointegration for investors, affect the optimal investment and consumption. The results show that when the two risk the prices of assets are undervalued, investors through borrowing to buy two risky assets. When two asset prices are overvalued, has a high degree of risk aversion of investors selling all Risk assets. When one of the prices of assets are overvalued, another asset price is undervalued, that investors take a "long - short" investment model in the financial market, which provides a theoretical support for pairs trading strategy in practice. Secondly, the stock returns in a short period of time has the momentum effect the time-varying characteristics, optimal investment and consumption problems of stock return existence of momentum. The momentum effect price model based on the whole life period of consumer utility maximization as the decision goal. In the unit intertemporal substitution elasticity coefficient, deduces the accurate value function, explicit expressions of the optimal investment and optimal consumption; in the intertemporal substitution elasticity coefficient is 1, the logarithmic linearization method, deduces the value function, the approximate analytical expression of the optimal investment and optimal consumption. On this basis, the use of Chinese stock market The parameter data of the model were calibrated and analyzed the influence of the momentum effect for optimal investment and optimal model of consumer behavior. The results show that the personal preference parameters, the relative level of risk aversion for the optimal investment strategy than the intertemporal substitution elasticity coefficient to the initial momentum; the value of the state variables from mild negative when the optimal investment demand is greater than zero, the intertemporal hedging demand is less than zero, and when the risk aversion coefficient is greater than 1, the intertemporal hedging demand occupies a significant weight in the total investment demand; when the momentum state variable initial value is moderate or negative when hedging demands is negative, the great to reduce the stock investment; and when the momentum of the initial values of state variable for the depth of the negative, intertemporal hedging demands for it, will greatly increase the investment in the stock. Personal preference parameters, cross period for Generation of elastic influence on optimal consumption wealth ratio than the risk aversion coefficient is important. Further, given the risk aversion coefficient, optimal consumption and wealth than is the intertemporal substitution elasticity coefficient decreasing function; given the intertemporal substitution elasticity coefficient, optimal consumption and wealth ratio is a decreasing function of the risk aversion coefficient. Thirdly, considering two investors face the same investment opportunity set optimal interactive portfolio decision problems. Using the stochastic volatility model of constant elasticity of variance to describe the "volatility smile" phenomenon. In the end time of investors personal wealth and wealth and the relative distance of the rival's weighted average utility maximization as the investment objectives, through random control the theory of general Hamilton-Jacobi-Bellman derived value function satisfies (HJB) equation. In the exponential utility and power utility function, derive the equilibrium strategy. Expression. On this basis, according to the different parameters of the model, the equilibrium strategy of exponential utility function is analyzed. The results showed that the equilibrium strategy for the investment period, the volatility of the stock return rate of the relevant parameters, the elastic coefficient, the coefficient of risk aversion of investors and the risk-free interest rate monotonic decreasing function; equilibrium strategy the initial stock price increasing function, and with the expected stock returns first increased and then decreased. Finally, in order to study the influence of random transformation of inflation and macroeconomic conditions for investment decision-making, established the Markov conversion mechanism of asset price model, using stochastic differential game theory, considering two investors face related but different investment the opportunity to set optimal portfolio decision problem. The interaction of two investors to maximize the wealth and the termination of time utility as the investment objectives, derived value The general Hamilton-Jacobi-Bellman function satisfy the equation (HJB). Further, with inflation in the power utility model, explicit expressions and equilibrium strategies derived value function Feynman-Kac said. No inflation in the exponential utility model, explicit expressions are also derived from the value function representation and Feynman-Kac equilibrium strategy. On the basis of in particular, discusses the two mechanism of state transition model, according to the different parameters of the model, analysis of the mechanism of conversion for effect. The results show that the macroeconomic state transition for the optimal portfolio strategy in a significant impact.

【學位授予單位】：湖南大學
【學位級別】：博士
【學位授予年份】：2016
【分類號】：F224;F830.59
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本文編號：1373480