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 Itˆo-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.

Keywords: Epstein–Zin utilities; forward utilities; forward recursive aggregators; forward performance processes; stochastic partial differential equations; convex duality; state price densities; optimal investment and consumption; 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; recursive utilities; Epstein-Zin utilities; stochastic partial differential equations; Heston model. (search for similar items in EconPapers)
Date: 2026-09-06
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