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An optimal consumption model with stochastic volatility

Author

Listed:
  • Wendell H. Fleming

    (Division of Applied Mathematics, Brown University, Providence, RI 02912, USA)

  • Daniel Hernández-Hernández

    (Centro de Investigación en Matemáticas, Apartado Postal 402, Guanajuato, Gto. 36000, México Manuscript)

Abstract

We consider an optimal consumption and investment model in continuous time, which is an extension of the original Merton's problem. In the proposed model, the asset prices are affected by correlated economic factors, modelled as diffusion processes. Writing the value function in a special form, it can be seen that another optimal control problem is involved and studying its associated HJB equation smoothness properties of the original value function can be derived as well as optimal policies.

Suggested Citation

  • Wendell H. Fleming & Daniel Hernández-Hernández, 2003. "An optimal consumption model with stochastic volatility," Finance and Stochastics, Springer, vol. 7(2), pages 245-262.
    • Handle: RePEc:spr:finsto:v:7:y:2003:i:2:p:245-262
    Note: received: November 2001; final version received: May 2002
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    More about this item

    Keywords

    Stochastic volatility; portfolio optimization; factor modelling; mean reverting;
    All these keywords.

    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • E2 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment
    • G1 - Financial Economics - - General Financial Markets

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