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An investment and consumption problem with CIR interest rate and stochastic volatility. (English) Zbl 1291.91189

Summary: We are concerned with an investment and consumption problem with stochastic interest rate and stochastic volatility, in which interest rate dynamic is described by the Cox-Ingersoll-Ross (CIR) model and the volatility of the stock is driven by Heston’s stochastic volatility model. We apply stochastic optimal control theory to obtain the Hamilton-Jacobi-Bellman (HJB) equation for the value function and choose power utility and logarithm utility for our analysis. By using separate variable approach and variable change technique, we obtain the closed-form expressions of the optimal investment and consumption strategy. A numerical example is given to illustrate our results and to analyze the effect of market parameters on the optimal investment and consumption strategies.

MSC:

91G10 Portfolio theory
60H30 Applications of stochastic analysis (to PDEs, etc.)
91B70 Stochastic models in economics
93E20 Optimal stochastic control
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