Vasicek利率模型下带有负债的投资组合优化

摘要：
研究随机利率模型下负债型投资组合优化问题的最优投资策略,其中假设无风险利率是遵循Vasicek利率模型的随机过程,而负债服从带漂移的布朗运动且与股票价格和利率存在相关性.应用动态规划原理得到满足值函数的哈密尔顿 雅可比 贝尔曼(HJB)方程,并进一步应用Legendre变换得到值函数的对偶方程,并研究了幂效用和指数效用函数下的最优投资策略.最后,应用分离变量和变量替换方法得到幂效用和指数效用函数下最优投资策略的显示表达式,并给出算例分析了市场参数对最优投资策略的影响.
关键词：
Vasicek利率模型; 负债过程; 动态规划原理; Legendre变换； 动态投资组合
中图分类号： F 830.59； O 211.63
文献标志码： A

Portfolio Optimization with Liability under the Vasicek Model

This paper is concerned with a portfolio optimization problem with liability and stochastic interest rate model, where risk-free interest rate is assumed to follow the Vasicek interest rate model, while liability process follows Brownian motion with drift. Moreover, it was assumed that liability dynamic is correlated with stock price and interest rate. Dynamic programming principle was applied to obtain Hamilton-Jacobi-Bellman(HJB) equation for the value function and further Legendre transform was used to derive its dual equation. Power utility and exponential utility function were chosen for the analysis. Finally, the closed-form solutions to the optimal investment strategies were obtained by using separate variable and variable change technique and numerical examples were presented to illustrate the impact of market parameters on the optimal policies.