Vasicek利率模型下带有零息票债券的投资-消费模型

Investment and Consumption Model with the Zero-Coupon Bond under the Vasicek Model

应用随机最优控制理论研究Vasicek利率模型下的投资-消费问题,其中假设无风险利率是服从Vasicek利率模型的随机过程,且与股票价格过程存在一般相关性.假设金融市场由一种无风险资产、一种风险资产和一种零息票债券所构成,投资者的目标是最大化中期消费与终端财富的期望贴现效用.应用变量替换方法得到了幂效用下最优投资-消费策略的显示表达式,并分析了最优投资-消费策略对市场参数的灵敏度.

This paper applied stochastic optimal control theory to investigate an investment and consumption problem with Vasicek interest rate model,in which interest rate was supposed to follow the Vasicek model and was generally correlated with stock price dynamics.Assuming that the financial market is composed of one risk-free asset and one risky asset and one zero-coupon bond,the obj ective of the investor is to maximize the expected discount utility of intermediate consumption and terminal wealth.By applying variable change approach,we obtained the closed-form solution of the optimal investment and consumption strategy in the power utility case.Finally,we provided a numerical example to illustrate the sensitivity of the optimal investment and consumption strategy on market parameters.