Ho-Lee利率模型下资产-负债管理的最优投资策略

假设无风险利率是服从Ho-Lee利率模型的随机过程,本文研究负债情形下组合投资的最优投资策略.我们考虑金融市场存在两种风险资产:一种股票和一种零息票债券,其中股票和零息票债券由于受到利率波动的影响而服从扩展的几何布朗运动,而负债服从扩展的带漂移的布朗运动,且和利率与股票价格存在相关性.文章应用最大值原理得到效用最大化下值函数的Hamilton-Jacobi-Bellman (HJB)方程,并研究幂效用和指数效用函数下的最优投资策略.利用变量变换方法得到了两种效用函数下最优投资策略的显示表达式.

Optimal Investment Strategy for Asset and Liability Management Problems under the Ho-Lee Interest Rate Model

Under the assumption that the risk-free interest rate dynamics follows the Ho-Lee interest rate model,we investigate the optimal investment strategy for portfolio selection with liability.The financial market is composed of two risky assets: a stock and a zero-coupon bond.The stock price and the bond price influenced by the interest rate volatility are all driven by the extended geometric Brownian motion.The liability process follows the extended Brownian motion with drift and is correlated with the interest rate and stock price.Under the utility maximization criterion,the maximum principle is used to obtain the HJB equation for the value function,and we study the optimal investment strategies under power utility and exponential utility,respectively.Finally,we obtain the closed-form solutions for the optimal investment strategies by applying the variable transformation approach.