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Mathematical Problems in Engineering
Volume 2016, Article ID 4823451, 12 pages
Research Article

Optimal Consumption and Portfolio Decision with Convertible Bond in Affine Interest Rate and Heston’s SV Framework

1School of Science, Tianjin Polytechnic University, Tianjin 300387, China
2College of Management and Economics, Tianjin University, Tianjin 300072, China

Received 27 January 2016; Accepted 22 May 2016

Academic Editor: Vladimir Turetsky

Copyright © 2016 Hao Chang and Xue-Yan Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We are concerned with an optimal investment-consumption problem with stochastic affine interest rate and stochastic volatility, in which interest rate dynamics are described by the affine interest rate model including the Cox-Ingersoll-Ross model and the Vasicek model as special cases, while stock price is driven by Heston’s stochastic volatility (SV) model. Assume that the financial market consists of a risk-free asset, a zero-coupon bond (or a convertible bond), and a risky asset. By using stochastic dynamic programming principle and the technique of separation of variables, we get the HJB equation of the corresponding value function and the explicit expressions of the optimal investment-consumption strategies under power utility and logarithmic utility. Finally, we analyze the impact of market parameters on the optimal investment-consumption strategies by giving a numerical example.