CEV模型下基于二次效用最大化的资产-负债管理模型（英文）

发布时间：2018-06-25 02:15

本文选题：CEV模型 + 资产-负债管理　；参考：《工程数学学报》2014年01期

【摘要】：本文研究CEV模型下基于效用最大化的资产-负债管理问题.文章假设股票价格服从CEV模型,而负债服从带漂移的布朗运动,且与股票价格存在一般相关性.应用动态规划原理得到值函数满足的HJB方程,并应用Legendre变换-对偶方法得到其对偶方程.假设投资人对风险的偏好满足二次效用函数,并应用变量替换方法得到最优投资组合的闭式解.结果表明:最优投资组合包含一个修正因子,该修正因子可影响投资人为对冲波动率风险而作出的投资决策.最后,文章分析了修正因子的性质并考察了修正因子对最优投资组合的影响.
[Abstract]:In this paper, we study the asset-liability management problem based on utility maximization in CEV model. This paper assumes that the stock price service follows the CEV model, while the debt service follows the Brownian motion with drift, and there is a general correlation between the stock price and the stock price. The HJB equation satisfying the value function is obtained by using the principle of dynamic programming, and the dual equation is obtained by using Legendre transform duality method. It is assumed that the investor's preference for risk satisfies the quadratic utility function, and the closed-form solution of the optimal portfolio is obtained by using the variable substitution method. The results show that the optimal portfolio contains a correction factor which can affect the investment decisions made by investors to hedge volatility risk. Finally, the properties of the correction factor are analyzed and the influence of the correction factor on the optimal portfolio is investigated.
【作者单位】：天津工业大学数学系;天津大学管理学院;天津大学理学院;
【基金】：The Humanities and Social Science Research Youth Foundation of Ministry of Education(11YJC790006) the Higher School Science and Technology Development Foundation of Tianjin(20100821)
【分类号】：F830.59;F224

【共引文献】