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arXiv · 2609.17053

Forward recursive aggregator systems and the forward Epstein-Zin recursiveparadigm

Zakaria Bensaid·Anis Matoussi·Thaleia Zariphopoulou
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Abstract

We introduce forward recursive aggregator systems in It__o-diffusion markets, bridging the theories of recursive utilities and of forward performance criteria. We derive the associated HJB SPDE and sufficient conditions for consistency and admissibility. We also develop a convex duality theory based on state price densities and identify the density generated by the optimal wealth process. For homothetic aggregators, we characterize a class of forward Epstein--Zin recursive utility processes, derive the optimal investment and consumption policies, and obtain explicit solutions in the Black and Scholes and Heston models.

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Zakaria Bensaid, Anis Matoussi, Thaleia Zariphopoulou. 2026-09-15. Forward recursive aggregator systems and the forward Epstein-Zin recursiveparadigm. https://arxiv.org/abs/2609.17053

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