本文选题：最优资产组合 + 最优消费资产组合 ； 参考：《湘潭大学》2017年硕士论文
【摘要】：1952年,H.Markowiz[1]发表的博士论文《Porofolio Selection》奠定了金融数学的理论基础.他将均值表示股票的收益,将协方差表示收益的风险,量化了股票市场“差异性”的概念.在金融资产中构造一个最优的资产组合,使得代表期望回报的均值和代表风险的方差达到最佳的平衡.也就是,给定资产的均值回报,应使得资产组合的方差最小;或者说是给定资产组合的协方差,应使得资产组合的均值回报最大.由此,最优资产组合理论的研究引起了众多学者的兴趣,对经典Markowiz资产组合问题做了许多进一步的拓展和应用.考虑到投资者不仅有资产组合活动,还会将财富进行消费.于是,Merton[2]讨论了最优消费投资组合问题,并且开创了随机最优控制方法.Merton假设金融模型时间连续,从此开始了连续时间资产组合理论.本文假设资产价格的变动服从带泊松跳的分数布朗运动,讨论了效用函数为幂函数的最优资产组合和最优消费资产组合.首先,在绪论中介绍了资产组合策略的历史和研究的意义,以及研究的成果.其次,在第二章中,预备知识的介绍,主要介绍的是几类基本的随机过程和随机分析中的分数布朗运动.然后,在第三章讨论了在假定的金融市场模型中,假设标的资产价格的变动服从带泊松跳的分数布朗运动,研究了最优资产组合中资产的配置比例.具体方法为:建立值函数,使得期末财富总量最大;运用动态规划原理,推导出HJB微分方程;最后得到最优资产组合的分配策略.此解可以给个人投资者在投资决策时提供有利的参考.第四章中,考虑了投资者在投资过程中的消费,此时的值函数为投资财富和累积消费的最大化.对最优消费资产组合的研究可以给投资者在投资消费过程中提供决策建议.最后,在第五章中,将本文的主要研究的工作内容与进展进行了简要的总结,并对接下来的研究方向进行了展望.
[Abstract]:In 1952, H.Markowiz[1]'s doctoral thesis,
, laid the theoretical basis for financial mathematics. He expressed the earnings of the stock, expressed the risk of the covariance, quantified the concept of the "difference" in the stock market, and constructed a best portfolio in the financial assets to make the mean value of the expected return. The variance of the representative risk reaches the best balance. That is, the mean return of a given asset should make the variance of the portfolio minimum; or the covariance of a given portfolio should make the average return of the portfolio maximum. Therefore, the study of the optimal portfolio theory has aroused the interest of many scholars and the classical Markowiz capital. The problem of production portfolio has been further expanded and applied. Considering that investors not only have portfolio activities, they will also consume wealth. So, Merton[2] discusses the optimal consumption portfolio problem and creates a stochastic optimal control method.Merton assuming that the financial model is a continuous time, and from then on, the continuous time asset group has been started. In this paper, this paper assumes that the change of asset price obeys the fractional Brown movement with Poisson jump, discusses the optimal portfolio of utility function as power function and the optimal combination of consumption assets. First, in the introduction, the history and significance of the portfolio strategy and the results of research are introduced in the introduction. Secondly, in the second chapter, the preparatory knowledge is prepared. This paper introduces several basic random processes and fractional Brown's motion in random analysis. Then, in the third chapter, we discuss the hypothesis that the change of the price of the underlying asset obeys the fractional Brown movement with Poisson jump, and studies the allocation ratio of the assets in the optimal asset portfolio. The vertical value function makes the total amount of the final wealth maximum; using the dynamic programming principle, the HJB differential equation is derived. Finally, the allocation strategy of the optimal portfolio is obtained. This solution can provide a favorable reference for individual investors to make investment decisions. In the fourth chapter, the consumption of investors in the investment process is considered, and the value function at this time is the investment wealth. The research on the optimal consumption asset portfolio can give investors decision making suggestions in the process of investment and consumption. Finally, in the fifth chapter, a brief summary is made on the work and progress of the main research in this paper, and the research direction of the docking is prospected.
【学位授予单位】：湘潭大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F830.9
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