时变金融市场下动态投资组合选择理论及其应用研究

发布时间：2018-01-03 10:23

  本文关键词：时变金融市场下动态投资组合选择理论及其应用研究　出处：《湖南大学》2016年博士论文　论文类型：学位论文

  更多相关文章： 动态投资组合选择 随机投资机会集 随机微分博弈 纳什均衡 跨期对冲需求

【摘要】：金融市场中充满了各种不确定性和时变性,投资者在投资中必然面临风险。怎样有效地控制和管理风险,如何通过分散化金融投资形成最优投资组合,有效地降低投资者面临的非系统性风险,就成为了投资者必须面对的一大挑战和难题。在现实中,不同的投资可能会产生不同的风险。特别的,短期投资者与长期投资者的最优投资需求是完全不一样的。通常短期投资者只关心在一个时期内的资产(组合)收益率的均值与风险,而忽略了投资机会集在下一个时期的可能变化,短期投资者的投资行为在这种情形下被认为是短视的。传统的资产组合选择理论忽略了投资机会集的变化和金融市场资产价格的时变特征对投资决策的影响。金融市场中大量的时变经验事实特征,比如,协整效应、动量效应、随机利率、随机波动率以及宏观经济状态随机转换都表明投资机会集不是固定不变的,而是具有随机性特征。实践中,投资者的投资行为通常是动态多期的,他们不只是关心当期投资机会集对于财富的冲击,而且关心投资机会集未来的随机性对于财富的跨期冲击。由于投资机会集随时间变化,投资者除了对金融资产的短视需求外,还具有跨期对冲需求,即利用金融资产来规避随机投资机会集的跨期冲击。因此,从长期视角出发,基于金融市场的多个时变特征,对动态投资组合选择问题的研究不仅具有重大的理论价值,也具有重要的现实意义。在这种背景下,本论文研究了基于多个不同金融市场特征下动态投资组合选择的若干问题,综合运用效用函数理论、随机控制理论和随机微分博弈理论,建立严格的数理金融模型,系统的探讨了模型特征、适用条件、投资与消费行为、跨期对冲需求、配对交易和动量投资策略等规律。主要研究成果简述如下:首先,针对股票价格之间的协整效应时变特征,研究了金融市场的股票资产存在协整关系的,投资者该如何进行投资与消费。基于协整资产价格模型,以有限期消费总效用和终端时刻财富期望效用的最大化为决策目标,分别在幂效用和对数效用函数下,推导出了最优化问题价值函数的高维、非线性、非齐次的Hamilton-Jacobi-Bellman(HJB)方程。给出了最优投资、最优消费的显式的表达式。讨论了动态优化模型的四种特殊情形:投资者只关心终端时刻的财富效用最大化;投资者只关心有限期的消费总效用最大化;股票价格之间不存在协整关系以及风险厌恶系数为零。在理论分析的基础上,分析了协整效应对于投资者的福利,最优投资与最优消费的影响。结果表明,当两个风险资产的价格都被低估时,投资者通过借贷买入两个风险资产。当两个风险资产的价格都被高估时,具有较高风险厌恶程度的投资者卖空全部的风险资产。当其中一个资产的价格被高估,另一个资产的价格被低估时,发现投资者在金融市场中采取一种“多头-空头”投资模式,这为实践中配对交易策略提供了理论支持。其次,针对股票收益在短时期内具有动量效应时变特征,研究了股票收益存在动量效应的最优投资和消费问题。基于动量效应价格模型,以整个生命期的消费效用最大化为决策目标。在单位跨期替代弹性系数下,推导出了价值函数、最优投资和最优消费的精确显式表达式;在跨期替代弹性系数不为1时,通过对数线性化方法,推导出了价值函数、最优投资和最优消费的近似解析表达式。在此基础上,利用中国股票市场数据对模型的参数进行了校准,分析了动量效应对于最优投资与最优消费行为模式的影响。研究结果表明,个人偏好参数中,相对风险厌恶水平对于最优投资策略的影响远比跨期替代弹性系数重要;在动量状态变量的初始值取温和的负值时,最优投资需求都大于零,跨期对冲需求小于零,并且当风险厌恶系数大于1时,跨期对冲需求在总的投资需求占有非常重要的权重;当动量状态变量初始值为正或者温和的负值时,跨期对冲需求为负,其极大的降低了股票上的投资;而当动量状态变量初始值为深度的负值时,跨期对冲需求为正,将极大的增加在股票上的投资。个人偏好参数中,跨期替代弹性对于最优消费财富比的影响远比风险厌恶系数重要。进一步,给定风险厌恶系数,最优消费与财富之比是跨期替代弹性系数的单调减函数;给定跨期替代弹性系数,最优消费与财富之比是风险厌恶系数的减函数。再次,考虑了两个投资者面对同一投资机会集时最优交互投资组合决策问题。利用常弹性方差随机波动率模型来描述“波动率微笑”现象。以投资者终止时刻个人的财富以及与竞争对手财富的相对距离的加权平均的效用最大化为投资目标,通过随机控制理论,推导出价值函数所满足的一般hamilton-jacobi-bellman(hjb)方程。在指数效用和幂效用函数下,推导出了均衡策略的显式表达式。在此基础上,针对不同的模型参数,对指数效用函数下的均衡策略进行了分析。结果发现,均衡策略为投资期限、股票收益的波动率相关参数、弹性系数、投资者自身的风险厌恶系数以及无风险利率的单调递减函数;均衡策略为股票初始价格的增函数,并且随股票的期望收益率先增后减。最后,为了研究通货膨胀和宏观经济状态的随机转换对于投资决策的影响,建立了马尔可夫机制转换资产价格模型,利用随机微分博弈理论,考虑了两个投资者面对相关但却不同的投资机会集时最优交互投资组合决策问题。以两个投资者终止时刻财富和的效用最大化为投资目标,推导出了价值函数所满足的一般hamilton-jacobi-bellman(hjb)方程。进一步,在幂效用带通胀的模型下,推导出价值函数的feynman-kac表示和均衡策略的显式表达式。在指数效用无通胀的模型下,也推导出价值函数feynman-kac表示和均衡策略的显式表达式。在此基础上,特别的讨论了两机制状态转换模型,针对不同的模型参数,分析了机制转换对于影响。结果显示,宏观经济状态转换对于最优投资组合策略存在着显著的影响。
[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.

【学位授予单位】：湖南大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：F224;F830.59
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本文编号：1373480