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Chinese Journal of Management Science ›› 2014, Vol. 22 ›› Issue (10): 29-37.

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

CHANG Hao1,2   

  1. 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

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

CLC Number: