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Optimal Consumption and Robust Portfolio Choice for the 3/2 and 4/2 Stochastic Volatility Models

Author

Listed:
  • Yuyang Cheng

    (Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, Canada
    These authors contributed equally to this work.)

  • Marcos Escobar-Anel

    (Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, Canada
    These authors contributed equally to this work.)

Abstract

This manuscript derives optimal consumption and investment strategies for risk-averse investors under the 4/2 stochastic volatility class of models. We work under an expected utility (EUT) framework and consider a Constant Relative Risk Aversion (CRRA) investor, who may also be ambiguity-averse. The corresponding Hamilton–Jacobi–Bellman (HJB) and HJB–Isaacs (HJBI) equations are solved in closed-form for a subset of the parametric space and under some restrictions on the portfolio setting, for complete markets. Conditions for proper changes of measure and well-defined solutions are provided. These are the first analytical solutions for the 4/2 stochastic volatility model and the embedded 3/2 model for the type of excess returns established in the literature. We numerically illustrate the differences between the 4/2 model and the embedded cases of the 1/2 model (Heston) as well as the 3/2 model under the same data, and for two main cases: risk-averse investor in a complete market with consumption, and ambiguity-averse investor in a complete market with no consumption. In general, the 4/2 and 1/2 models recommend similar levels of consumption and exposure, while the 3/2 leads to significantly different recommendations.

Suggested Citation

  • Yuyang Cheng & Marcos Escobar-Anel, 2023. "Optimal Consumption and Robust Portfolio Choice for the 3/2 and 4/2 Stochastic Volatility Models," Mathematics, MDPI, vol. 11(18), pages 1-28, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:4020-:d:1245070
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    References listed on IDEAS

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