Abstract
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.
Highlights
As a hot topic, investment-consumption problem has abstracted increasing attention of many investment institutions which include insurance companies, pension management institutions, and commercial banks
This paper considers the impact of interest rate on stock price and extends the model of Chang and Rong [24] and further studies a general investment-consumption problem with stochastic interest rate and stochastic volatility
We studied optimal consumption and portfolio decision with affine interest rate and stochastic volatility
Summary
Investment-consumption problem has abstracted increasing attention of many investment institutions which include insurance companies, pension management institutions, and commercial banks. Liu [22] and Noh and Kim [23] investigated the optimal consumption-investment problems with stochastic interest rate and stochastic volatility, but they did not obtain the explicit solutions to the optimal consumption-investment strategies. Chang and Rong [24] studied a special optimal investment-consumption problem with CIR interest rate and stochastic volatility under the assumption that interest rate dynamics are independent of stock price dynamics. This paper considers the impact of interest rate on stock price and extends the model of Chang and Rong [24] and further studies a general investment-consumption problem with stochastic interest rate and stochastic volatility.
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