短期和长期债券最优配置连续时间模型的理论分析（英文）  

Theoretical Analysis for Continuous-time Models of the Optimal Allocation of Short-term and Long-term Bonds

作　　者：梁治安[1] 王燕军[1] 谢瑶[2] 

机构地区：[1]上海财经大学数学学院,上海200433 [2]上海财经大学金融学院,上海200433

出　　处：《内蒙古大学学报（自然科学版）》2015年第1期1-11,共11页Journal of Inner Mongolia University：Natural Science Edition

基　　金：Supported by Shanghai Pujiang Program(11PJC059);Innovation Program of Shanghai Municipal Education Commission(12ZZ071);the National Natural Science Foundation of China(NSFC 11271243)~~

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.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.

关 键 词：债券最优配置 真实利率波动 投资组合 

分 类 号：F830.59[经济管理—金融学]