论文部分内容阅读
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.
This paper studies asset-liability management based on maximization of utility under the CEV model.The article assumes that the stock price obeys the CEV model and the debt obeys the Brownian motion with drift, and is generally related to the stock price.Applying the dynamic programming principle to obtain the value function satisfies The HJB equation is obtained and its duality equation is obtained using the Legendre transformation-dual method. Suppose 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 investment The portfolio includes a correction factor that can influence the investor’s investment decisions for hedging risk.Finally, the article analyzes the nature of the correction factor and examines the effect of the correction factor on the optimal portfolio.