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

  • Zakaria Bensaid
  • Anis Matoussi
  • Thaleia Zariphopoulou
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Abstract

We introduce forward recursive aggregator systems in It{ô}-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.

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Cite

BibTeXRIS
BibTeX
@misc{bensaid2026forward,
  title = {{Forward recursive aggregator systems and the forward Epstein-Zin recursive paradigm}},
  author = {Zakaria Bensaid and Anis Matoussi and Thaleia Zariphopoulou},
  howpublished = {HAL},
  year = {2026},
  month = jul,
  doi = {10.48550/arxiv.2609.17053},
  eprint = {2609.17053},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05735109v3},
}
RIS
TY  - UNPB
TI  - Forward recursive aggregator systems and the forward Epstein-Zin recursive paradigm
AU  - Zakaria Bensaid
AU  - Anis Matoussi
AU  - Thaleia Zariphopoulou
PY  - 2026
DA  - 2026/07/27
PB  - HAL
DO  - 10.48550/arxiv.2609.17053
UR  - https://hal.science/hal-05735109v3
AB  - We introduce forward recursive aggregator systems in It{ô}-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.
ER  -