WSEAS Transactions on Mathematics
Print ISSN: 1109-2769, E-ISSN: 2224-2880
Volume 15, 2016
Optimal Consumption and Portfolio Decisions with Stochastic Affine Interest Rate Model
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Abstract: This article is concerned with an investment and consumption problem with stochastic affine interest rate model, which includes the CIR model and the Vasicek model as special cases. The financial market is composed of three assets: one cash account, one stock and one zero-coupon bond. Moreover, the price dynamics of the stock and zero-coupon bond is affected by the dynamics of interest rate. Our objective is to seek an optimal consumption and portfolio decisions to maximize the expected discounted utility of intermediate consumption and terminal wealth in the finite horizon. By applying stochastic dynamic programming principle and variable change techniques, we obtain the explicit expressions of the optimal consumption and portfolio decisions in the power utility and logarithm utility cases. In order to analyze the impact of the parameters of interest rate on the optimal consumption and portfolio decisions, we provide a numerical example to illustrate our results.
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Keywords: Investment and consumption, stochastic affine interest rate model, stochastic dynamic programming principle, the closed-form solution
Pages: 96-109
WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 15, 2016, Art. #10