基于g-期望的动态投资组合研究

发布时间：2018-03-19 21:12

本文选题：Hull-White随机利率　切入点：时变波动率　出处：《山东科技大学》2017年硕士论文　论文类型：学位论文

【摘要】：在投资组合理论中,最优投资组合问题一直是学者们的研究热点。起初,投资组合理论是在线性期望的框架下展开的,但是,由于现实金融环境中的不确定性、投资者的偏好差别等,线性期望框架下的投资组合也就有了一定的局限性,所以我们需进一步研究非线性期望框架下的最优投资组合问题,同时,金融产品的多样化也需要我们将衍生证券考虑到投资组合问题的研究中。本文主要研究了两个问题,一是在线性期望框架下,初步研究了基于随机利率和时变波动率的股票和债券的动态投资组合;另一个是在g-期望框架下,进一步研究了基于随机利率和时变波动率的股票、债券和衍生证券的动态投资组合。本文主要分为五部分:第一章论述了研究背景、国内外研究现状及研究内容和框架;第二章准备工作介绍了动态规划法、效用函数和三种效用模型、Ito积分和随机微分方程、g-期望;第三章在线性期望框架内,动态投资组合的研究考虑了 Hull-White随机利率和时变波动率,最后在效用函数为幂效用函数时推出最优投资策略;第四章在g-期望框架下,考虑Hull-White利率和时变波动率的同时,引进了衍生证券,并推出最优投资策略,最后推出了效用函数分别为幂效用函数和指数效用函数时的最优投资策略的表达式;第五章做出了总结和展望,并阐述了本文的不足和此后的研究方向。
[Abstract]:In portfolio theory, the optimal portfolio problem has always been a hot topic for scholars. At first, portfolio theory was developed under the framework of linear expectation, but because of the uncertainty in the real financial environment, The difference of investor's preference and so on, the investment portfolio under the linear expectation frame also has the certain limitation, therefore we need to further study the optimal portfolio problem under the non-linear expectation frame, at the same time, The diversification of financial products also requires us to take derivative securities into account in the study of portfolio problems. The dynamic portfolio of stocks and bonds based on stochastic interest rate and time-varying volatility is studied preliminarily. The other is the further study of stocks based on stochastic interest rate and time-varying volatility under the framework of g-expectation. Dynamic portfolio of bonds and derivative securities. This paper is divided into five parts: the first chapter discusses the research background, domestic and foreign research status, research content and framework, the second chapter introduces the dynamic programming method. The utility function and three utility models are Ito integral and stochastic differential equations. In chapter 3, the Hull-White stochastic interest rate and the time-varying volatility are considered in the study of dynamic portfolio within the framework of linear expectation. Finally, when the utility function is the power utility function, the optimal investment strategy is proposed. Chapter 4th introduces the derivative securities and the optimal investment strategy under the framework of g- expectation, considering the Hull-White interest rate and the time-varying volatility. Finally, the expressions of optimal investment strategy when utility function is power utility function and exponential utility function are derived. Chapter 5th makes a summary and prospect, and expounds the deficiency of this paper and the research direction in the future.
【学位授予单位】：山东科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：F224;F830.91

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