Ho-Lee利率模型下带有零息票债券的投资-消费模型

中国管理科学 ›› 2014, Vol. 22 ›› Issue (10): 29-37.

Ho-Lee利率模型下带有零息票债券的投资-消费模型

常浩^1,2

1. 天津工业大学理学院, 天津 300387;
2. 天津大学管理与经济学部, 天津 300072

收稿日期:2012-12-11 修回日期:2013-07-03 出版日期:2014-10-20 发布日期:2014-10-20
作者简介:常浩（1979-），男（汉族），天津工业大学数学系，博士，副教授，研究方向：金融系统工程、数学建模.
基金资助:
中国博士后科学基金面上项目（2014M560185）；教育部人文社会科学研究青年基金资助项目（11YJC790006）

Investment and Consumption Model with the Zero-Coupon Bond under the Ho-Lee Interest Rate Model

CHANG Hao^1,2

1. Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China;
2. College of Management and Economics, Tianjin University, Tianjin 300072, China

Received:2012-12-11 Revised:2013-07-03 Online:2014-10-20 Published:2014-10-20

摘要/Abstract

摘要： 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。

关键词: Ho-Lee利率模型, 投资-消费模型, 动态规划原理, 幂效用, 对数效用

Abstract: A class of continuoue-time investment-consumption problems are studied with stochastic interest rate environment and zero-coupon bond, in which risk-free interest rate is driven by the Ho-Lee interest rate model and financial market is composed of one risk-free asset and one risky asset and one zero-coupon bond. The investor wishes to choose an optimal investment-consumption strategy to maximize the expected discounted utility of terminal wealth and consumption. The explicit expressions of the optimal investment-consumption strategies in the power and logarithm utility cases are obtained by applying dynamic programming principle and variable change approach. A numerical example is given to illustate the dynamic behavior of the optimal investment-consumption strategy with respect to market parameters and some economic implications are achieved.

Key words: Ho-Lee interest rate model, investment and consumption model, dynamic programming principle, power utility, logarithm utility

中图分类号:

常浩. Ho-Lee利率模型下带有零息票债券的投资-消费模型[J]. 中国管理科学, 2014, 22(10): 29-37.

CHANG Hao. Investment and Consumption Model with the Zero-Coupon Bond under the Ho-Lee Interest Rate Model[J]. Chinese Journal of Management Science, 2014, 22(10): 29-37.

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