在随机利率环境下研究一类带有零息票债券的投资-消费问题,其中假设无风险利率是服从Ho-Lee利率模型的随机过程,且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。投资人希望选择一种最优投资-消费策略来最大化其有限时间段内终端财富和累积消费的期望效用。文章应用动态规划原理和变量替换方法得到了幂效用和对数效用下最优投资-消费策略的显示解。算例分析演示了最优投资-消费策略随市场参数的变化而变化的动态行为,并给出了一些经济学涵义。 In a stochastic interest rate environment, we study a kind of investment-consumption problem with zero-coupon bonds, in which the risk-free rate is assumed to be a stochastic process subject to the Ho-Lee interest rate model, and the financial market consists of a risk-free asset, a risk asset And a zero-coupon bond. Investors want to choose an optimal investment-consumption strategy that maximizes the expected utility of terminal wealth and cumulative consumption for a limited period of time. In this paper, we apply the dynamic programming principle and the variable substitution method to obtain the optimal solutions of power consumption and logarithm utility. The case study demonstrates the dynamic behavior of the optimal investment-consumption strategy with the change of market parameters, and gives some economic implications.