CEV模型下基于二次效用最大化的资产-负债管理模型（英文）  

CEV Model for Asset and Liability Management under Quadratic Utility Maximizing Criterion

作　　者：常浩[1,2] 荣喜民[3] 赵慧[3] 

机构地区：[1]天津工业大学数学系,天津300387 [2]天津大学管理学院,天津300072 [3]天津大学理学院,天津300072

出　　处：《工程数学学报》2014年第1期112-124,共13页Chinese Journal of Engineering Mathematics

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)

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.In this paper, we consider an asset and liability management problem under the utility maximizing criterion, in which stock price is assumed to comply with the constant elasticity of variance （CEV） model, while liability follows the Brownian motion with drift, and liability and stock price are generally correlated between each other. We apply the dynamic programming principle to solving the HJB equation for the value function and use the Legendre transform-dual technique to transform the HJB equation into its dual equation. Furthermore, we choose a quadratic utility function for our analysis and obtain the closed-form solution to the optimal portfolio by applying the variable change approach. The result indicates that the optimal portfolio includes a modified factor which is capable of reflecting an investor’s decision to hedge the volatility risk. Finally, we analyze the property of the modified factor and investigate its effect on the optimal portfolio.

关 键 词：CEV模型 资产-负债管理 二次效用 LEGENDRE变换 最优投资组合 

分 类 号：F832.8[经济管理—金融学] O211.6[理学—概率论与数理统计]