Robustness meets co-jumps: optimal consumption and portfolio choice with derivatives

Immacolata Oliva and Ilaria Stefani

Quantitative Finance, 2024, vol. 24, issue 12, 1799-1822

Abstract: In this paper, we study a robust, dynamic, continuous-time optimal consumption and portfolio allocation problem for investors with recursive preferences who have access to both stock and derivatives markets. We assume the stock price process follows a stochastic volatility model, with instantaneous precision as the unique state variable, allowing for discontinuities in all the dynamics. We obtain a closed-form approximate solution up to a system of ODEs to the optimization problem for a non-unitary value of the elasticity of intertemporal substitution of consumption, being able to derive an exact solution as a particular case. Our theoretical findings show that the optimal policies are remarkably affected by the ambiguity-aversion parameters to diffusive and jump risks. A detailed numerical analysis confirms the effectiveness of our theoretical results on real data. Finally, we prove that investors who do not believe in ambiguity may suffer considerable wealth losses.

Date: 2024
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DOI: 10.1080/14697688.2024.2410862

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