Forward recursive aggregator systems and the forward Epstein-Zin recursive paradigm

Zakaria Bensaid, Anis Matoussi () and Thaleia Zariphopoulou
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Zakaria Bensaid: LMM - Laboratoire Manceau de Mathématiques - UM - Le Mans Université
Anis Matoussi: LMM - Laboratoire Manceau de Mathématiques - UM - Le Mans Université
Thaleia Zariphopoulou: Departments of Mathematics and IROM, The University of Texas at Austin, Austin,

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Abstract: We introduce forward recursive aggregator systems in Itô-diffusion markets, bridging the theories of recursive utilities and of forward performance criteria. The resulting criteria are constructed forward in time and accommodate arbitrary or rolling horizons. 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.

Keywords: state price densities; Heston model.; stochastic partial differential equations; Epstein-Zin utilities; recursive utilities; recursive utilities Epstein-Zin utilities forward utilities forward recursive aggregators forward performance processes stochastic partial differential equations convex duality state price densities optimal investment and consumption Heston model; optimal investment and consumption; convex duality; stochastic partial differential equations; forward performance processes; forward recursive aggregators; forward utilities; Epstein–Zin utilities (search for similar items in EconPapers)
Date: 2026-09-02
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