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

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  • Hao Chang
  • Xi-min Rong

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.

Suggested Citation

  • Hao Chang & Xi-min Rong, 2013. "An Investment and Consumption Problem with CIR Interest Rate and Stochastic Volatility," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, May.
    • Handle: RePEc:hin:jnlaaa:219397
    DOI: 10.1155/2013/219397
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    Cited by:

    1. Yumo Zhang, 2023. "Utility maximization in a stochastic affine interest rate and CIR risk premium framework: a BSDE approach," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 46(1), pages 97-128, June.

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