An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility

Hao Chang and Xi-min Rong

Abstract and Applied Analysis, 2013, vol. 2013, 1-12

Abstract:

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:219397

DOI: 10.1155/2013/219397

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