【摘要】 讨论短期长期零息债券在连续时间下的最优投资组合模型.采用Cox-Ingersoll-Ross模型描述短期无风险利率的动态过程,并且在随机利率模型下,长期零息债券的回报率服从一个扩散过程,它的漂移项和扩散项都是短期无风险利率的函数.假设投资者在资金预算约束下最大化他们的效用,用动态规划和秧方法解这个动态选择问题;用线性逼近的方法求解价值函数和投资财富函数的偏微分方程,并且得到最优消费和投资组合的解析解.更多还原

【Abstract】 Optimal portfolio of short-term and long-term zero coupon bonds under continuous time is discussed.A Cox-Ingersoll-Ross model is applied to describe the dynamic process of short risk-free interest rate,and under this stochastic interest rate model,the return of long-term zero coupon bond follows a diffusion process,whose shift and diffusion are both functions of short risk-free interest rate.Investors maximize their utility under budget constraint and the dynamic choice problem is solved by dynamic programming and martingale method.By a linear approximate method,partial differential equations of value function and optimal investment wealth function are solved,and explicit solutions of optimal consumption and portfolio are obtained.更多还原