均值—方差准则下连续时间证券投资选择研究

发布时间：2018-02-23 23:46

本文关键词： 均值-方差准则预定策略时间一致策略均衡值函数　出处：《天津大学》2014年博士论文　论文类型：学位论文

【摘要】：众所周知，马克维茨所建立的均值-方差方法是现代金融理论的基石。2000年以前，学者主要处理的是单期情形下的证券投资选择问题，在多期投资和连续期限投资时，均值-方差问题演变为时间不一致问题，从而导致传统意义下的动态规划原理不再成立。现在流行两种解决此类最优控制问题的基本方法:第一种方法称为预定策略法。决策者在初始时刻选择一种策略，并且在以后的时间内都按照此策略投资；第二种方法是基于博弈论思想来研究此类问题。时间不一致问题的解释是随着时间推移策略变动不仅仅依赖于时间，还依赖于其它初始变量，将此类时间不一致问题看成一个博弈问题，将博弈系统中的选手看成在将来各时刻具有决策权的投资人的化身，最终找到此类时间不一致问题的纳什均衡点。第二章主要在均值方差准则下研究对偶风险模型的最优投资选择问题。假定金融市场由一种无风险资产（债券）和一种风险资产（股票）构成，在卖空和借贷不加限制情形下研究最优预定策略和时间一致策略。首先，采用拉格朗日技术来得出最优预定策略，所采用的方法与Zhou,Li(2000)和Li, Ng (2000)提出的嵌入技术有所不同，我们的方法更简便并更好理解；其次，基于Bj o¨rk, Murgoci (2010)提出的博弈论技术，得到了对偶风险模型下的时间一致投资策略。最后，对预定最优策略和时间一致策略进行比较，并解释了两者的优劣：预定策略尽管能够使得均值-方差目标函数最大化，但是它不是时间一致策略。第三章通过整合经典风险模型和对偶模型，构建广义风险模型，，将金融市场扩展到由一种无风险资产和多种风险资产构成，首先，采用第二章类似的拉格朗日技术，得出广义风险模型的最优预定策略；其次基于博弈论视角，通过求解广义哈密尔顿-雅可比-贝尔曼方程，求得时间一致投资策略；最后，从理论角度和数值方面展示了各参数对最优投资策略和相应值函数的影响，并对最优预定策略和最优时间一致策略进行比较得到，持有时间一致策略下的公司为了在所有时刻t都能获得稳定收益，而不得不放弃在初始时刻所能获得的最大利益。第四章推广了Bj o¨rk, Murgpci, Zhou(2012)提出的投资组合模型。金融市场由一种无风险资产和n种风险资产构成，在状态相依风险厌恶系数假定下研究公司的投资组合问题，得到资产配置的最优预定投资策略和最优时间一致投资策略，从理论角度和数值方面展示了各参数对最优预定投资策略和相应值函数的影响，并且从数值方面展示了各参数对时间一致投资策略和相应均衡值函数的影响。第五章在均值方差准则下，研究对偶风险模型和对偶扩散风险模型的投资问题。公司在跳扩散金融市场(风险资产价格服从跳扩散随机微分方程)中投资，基于博弈论角度来处理此类时间不一致问题，在经典对偶风险模型和对偶扩散风险模型下，得到该问题时间一致投资策略和均衡值函数的解析解。
[Abstract]:As everyone knows, the mean Markowitz variance method is established by the modern financial theory cornerstone.2000 years ago, scholars mainly deal with the problem of portfolio selection under the condition of single period, multi period investment and investment in the continuous period, the mean variance problem for the evolution of the time inconsistency problem, which leads to the traditional dynamic programming principle the sense is no longer valid. Two kinds of basic methods to solve the optimal control problem is popular now: the first method is called the method of predetermined strategy. Decision makers choose a strategy at the initial time, and at a later time in accordance with the strategy of investment; the second method is the problem of this kind of game theory based on time. The inconsistency is the explanation of the strategy change time depends not only on time, but also depends on other initial variables, such as the time inconsistency problem of a game ask The players in the game system are regarded as the investors of the decision-making power at any time in the future, and finally find the Nash equilibrium point of such a time inconsistent problem.
The optimal investment problem of the second chapter mainly studies the dual risk model in the mean variance criterion. We assume that the financial market is a risk-free asset (bonds) and a risk assets (stocks), in short selling and borrowing unrestricted case of optimal reservation strategy and time consistent strategies. First, to derive optimal reservation the strategy of Lagrange technology, and Zhou methods, Li and Li (2000), Ng (2000) proposed the embedded technology is different, our method is more simple and better understanding; secondly, based on the "rk Bj o, Murgoci (2010) put forward the technology of game theory, the dual risk model. The same time investment strategy. Finally, to compare the predetermined optimal strategy and time consistent strategy, and explains the advantages and disadvantages of the two strategies: Although the predetermined can make the mean variance maximization of the objective function, but it is not a time Make a strategy.
The third chapter through the integration of the classical risk model and the dual model, the construction of generalized risk model, will be extended to the financial market by a risk-free asset and multiple risky assets, first of all, using the Lagrange technique in chapter second similar, we obtained the optimal generalized risk model intended strategy based on Game theory; secondly, by solving the generalized Jacobi - Hamilton Behrman equation, obtain the time consistent investment strategy; finally, from the perspective of theory and numerical display of the parameters on the optimal investment strategy and the corresponding value function and the optimal pre setting strategy and optimal time consistent strategies are compared, the same time the strategy of holding company in order to get a stable income at all times T, and had to give up the maximum benefit can be obtained at the initial time.
The fourth chapter generalizes Bj o "rk, Murgpci, Zhou (2012) portfolio model is put forward. The financial market by a risk-free asset and N kinds of risk assets, the risk aversion coefficient dependent portfolio problem under the assumption of the company in the state, the optimal asset allocation by pre fixed investment strategy and the optimal time investment strategy, from the angle of theory and numerical show on the optimal investment strategy and the corresponding predetermined value function and the effects of various parameters, from the numerical display of various parameters on the same time investment strategy and the corresponding equilibrium value function.
In the fifth chapter, the mean variance criterion, study the dual risk model and dual diffusion risk model with investment problem. Companies in financial markets (jump diffusion price risk assets obeying jump diffusion stochastic differential equation) in investment, based on the perspective of game theory to deal with this kind of time inconsistency, in the classical risk model and dual dual diffusion risk model the same time, investment strategies and equilibrium value function analytic solution.

【学位授予单位】：天津大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：F830.91;F224

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