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

Yuyang Cheng and Marcos Escobar-Anel ()
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Yuyang Cheng: Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, Canada
Marcos Escobar-Anel: Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON N6A 5B7, Canada
Authors registered in the RePEc Author Service: Marcos Escobar Anel ()

Mathematics, 2023, vol. 11, issue 18, 1-28

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.

Keywords: 4/2 stochastic volatility; CRRA (power) utility; optimal portfolio investment and consumption; Heston’s model; 3/2 model (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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