带有Markov调制参数的投资组合选择模型研究

发布时间：2018-06-23 15:02

本文选题：投资组合 + 随机LQ控制　；参考：《西安工程大学》2012年硕士论文

【摘要】：由Markowitz提出的证券投资组合模型是现代投资理论的基石，论文主要内容是对带有Markov调制参数的证券投资组合选择模型的研究，论文首先研究了带有Markov调制参数的离散时间LQG完全状态信息情况，其次，给出了带有Markov调制参数的随机LQ控制的最优控制策略及其应用，此外，论文研究了金融市场上处于竞争状态下小投资者在有利与不利条件下证券投资组合的选择模型，给出了其最优投资组合策略。最后，论文还研究了带有Markov调制参数的条件破产概率问题，给出了条件破产概率满足的一个偏微分方程，并在随机利率条件下作了进一步深入研究。全文主要内容共分为六章： (1)第一章介绍了带有Markov调制参数的投资组合选择问题的研究意义及研究现状，并简单介绍了本论文的所解决的问题和主要研究内容。 (2)第二章主要介绍了本论文研究过程中应用的主要工具，涉及的重要引理和定义。 (3)第三章研究内容是带有Markov调制参数的离散时间LQG完全状态信息情况，论文将Markov体制转换引入离散时间线性二次型高斯（LQG）完全状态信息情况原模型中，主要是考虑到现实生活中宏观经济条件下体制转换会对状态因素产生影响，引入有限Markov链更具有现实意义，最后论文利用贝尔曼动态规划法给出其最优控制策略。 (4)第四章研究的是带有Markov调制参数的随机LQ框架，在随机LQ控制模型中考虑状态因素的影响，论文将该模型推广到系统状态为跳跃-扩散过程的随机LQ控制，并引入跳-扩散的随机Riccati方程及连续时间Markov链，然后应用随机变分法求得问题的最优反馈控制策略。最后论文运用该模型去处理了金融中借贷利率不等和非自融条件下的最优投资组合问题和套期保值问题，分别得到了他们的有效投资组合策略。 (5)第五章在如下的金融市场上研究了投资策略的选择问题：设金融市场中有一种无风险证券（假设为债券），两种风险证券（假设为股票），投资者A,B均只能在一种风险证券与无风险证券上进行投资，以两个投资者财富之比为对策状态变量，构成零和随机对策。论文在风险价格表达式中引入了Markov链，研究了投资者在有利与不利条件下证券组合选择的竞争模型,最终得到了其最优投资组合策略。 (6)第六章研究了条件破产概率问题，论文将Markov链引入模型，，并将盈余过程推广到跳-扩散过程，应用It'o公式和鞅方法得到了有限条件破产概率满足的一个偏微分方程，然后论文在随机利率条件下做了进一步研究。
[Abstract]:The portfolio model proposed by Markowitz is the cornerstone of modern investment theory. The main content of this paper is to study the portfolio selection model with Markov modulation parameters. Firstly, the complete state information of discrete time LQG with Markov modulation parameters is studied. Secondly, the optimal control strategy of stochastic LQ control with Markov modulation parameters and its application are given. This paper studies the portfolio selection model of small investors in the competitive state of financial market under favorable and unfavorable conditions, and gives the optimal portfolio strategy. Finally, the conditional ruin probability problem with Markov modulation parameters is studied, and a partial differential equation of conditional ruin probability is given, which is further studied under the condition of stochastic interest rate. The main contents of this paper are divided into six chapters: (1) Chapter 1 introduces the significance and research status of portfolio selection with Markov modulation parameters. And briefly introduced the problems solved in this paper and the main research content. (2) the second chapter mainly introduces the main tools used in the research process of this paper. (3) in Chapter 3, the discrete time LQG complete state information with Markov modulation parameters is studied. In this paper, Markov system transformation is introduced into the original model of discrete time linear quadratic Gao Si (LQG) complete state information. It is more practical to introduce finite Markov chain. In the end, the optimal control strategy is given by using Berman dynamic programming method. (4) in chapter 4, the stochastic LQ frame with Markov modulation parameters is studied. Considering the influence of state factors in the stochastic LQ control model, the model is extended to the stochastic LQ control in which the state of the system is a hopping diffusion process, and the stochastic Riccati equation of hopping diffusion and the continuous time Markov chain are introduced. Then the optimal feedback control strategy of the problem is obtained by using the stochastic variational method. Finally, this paper uses the model to deal with the optimal portfolio problem and hedging problem under the condition of unequal lending rate and non-self-financing. (5) in chapter 5, we study the choice of investment strategies in the following financial markets: let there be a risk-free security in the financial market (assuming bonds), two kinds of investment strategies are obtained. (5) in the fifth chapter, we study the choice of investment strategies in the following financial markets: let there be a risk-free security in the financial market (assuming bonds). Risk securities (assuming stocks), investors AWAB can only invest in a risky and risk-free securities, Taking the ratio of the two investors' wealth as the game state variable, the zero sum stochastic game is formed. In this paper, Markov chain is introduced into the expression of risk price, and the competitive model of portfolio selection for investors under favorable and unfavorable conditions is studied. Finally, the optimal portfolio strategy is obtained. (6) in Chapter 6, the conditional ruin probability problem is studied. Markov chain is introduced into the model, and the surplus process is extended to the jump-diffusion process. In this paper, we obtain a partial differential equation with finite ruin probability by using ITO formula and martingale method, and then we study it further under the condition of stochastic interest rate.
【学位授予单位】：西安工程大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F830.91;F224

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