跳—扩散过程下的资产—负债模型研究

发布时间：2018-05-16 15:53

本文选题：投资组合 + 跳-扩散过程　；参考：《暨南大学》2014年硕士论文

【摘要】：在金融投资理论中，，投资组合管理是一个备受关注的研究课题，是现代金融工程的重要研究内容。而资产-负债管理又是现代投资组合管理和风险管理的重要研究领域之一，受到越来越多的重视。 Sharpe和Tint(1990)首次将负债引入到投资组合管理中，研究了负债情形下的均值-方差投资组合选择模型，为资产-负债管理的后续分析奠定了理论基础；Xie和Li(2008)等人对多个风险资产和一个负债在不完全市场下，且具有连续时间的均值-方差投资组合选择模型进行了研究，得到了最优投资组合策略和均值-方差模型的有效解。本文是在Xie和Li等人的工作基础上，在已有的资产模型中加入带跳部分，研究了跳-扩散过程下资产-负债模型的投资组合问题。相比于Xie和Li等人的研究方法与思路，本文是基于不完全市场背景下的投资组合研究，使用降维的方法让不完全市场转化为完全市场；在资产模型中引入跳跃部分，且带跳跃的资产与负债存在相关关系，利用随机控制论中的动态规划理论并结合HJB方程，求解出了满足目标函数的最优投资比例和投资组合期望收益，即给出了跳-扩散过程下资产-负债模型的最优投资策略和投资组合期望收益的解析表达式；同时还考虑了跳-扩散过程下基于不同利率的资产-负债模型，并研究了此类问题的风险管理和最优投资组合问题。本文的研究可视为对资产-负债管理问题的一个自然延伸与推广。
[Abstract]:In the theory of financial investment, portfolio management is a subject of great concern and an important research content of modern financial engineering. Asset-liability management is one of the most important research fields in modern portfolio management and risk management. Sharpe and Tint 1990) introduced debt into portfolio management for the first time, and studied the mean-variance portfolio selection model in the case of debt. It lays a theoretical foundation for the follow-up analysis of asset-liability management, such as Xie and Li, et al., and studies the mean-variance portfolio selection model of multiple risky assets and a liability in incomplete market with continuous time. The optimal portfolio strategy and the efficient solution of the mean-variance model are obtained. In this paper, based on the work of Xie and Li et al., the portfolio problem of asset-liability model in the jump-diffusion process is studied by adding a jump part to the existing asset model. Compared with the research methods and ideas of Xie and Li et al., this paper is based on portfolio research in the context of incomplete market, using dimensionality reduction method to transform incomplete market into complete market, and introducing jump part into asset model. Moreover, there is a correlation between assets with jump and liabilities. By using the dynamic programming theory in stochastic cybernetics and HJB equation, the optimal investment ratio and the expected return of the portfolio are obtained, which satisfy the objective function. The analytical expressions of the optimal investment strategy and the expected return of the portfolio are given, and the asset-liability model based on different interest rates is also considered in the jump-diffusion process. The risk management and optimal portfolio problem of this kind of problems are studied. The study of this paper can be regarded as a natural extension and extension of asset-liability management problem.
【学位授予单位】：暨南大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.59

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