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PreprintCC BY 4.0arXiv

Mean-field quadratic BSDEs and related mean-field portfolio games of controls

  • Huilin Zhang
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Abstract

We study a new class of mean-field quadratic backward stochastic differential equations (qBSDEs) arising from mean-field portfolio games with exponential utility. Typical examples of such games include a mean-field portfolio game with price impact, and a finite-contract pricing model with market clearing conditions. Generators of these mean-field qBSDEs contain quadratic terms 𝔼[Z]⊤ Z and |𝔼[Z]|2, instead of the classical pathwise Z⊤ Z term. We prove local well-posedness under Lq-integrability assumptions on terminals and their Malliavin derivatives, and global well-posedness under an extra exponential integrability condition on the Malliavin derivatives. Then we show the existence and uniqueness of global equilibria of the above two mean-field games via our qBSDE theory.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026meanfield,
  title = {{Mean-field quadratic BSDEs and related mean-field portfolio games of controls}},
  author = {Huilin Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07909},
  eprint = {2609.07909},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07909},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Mean-field quadratic BSDEs and related mean-field portfolio games of controls
AU  - Huilin Zhang
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07909
UR  - https://arxiv.org/abs/2609.07909
AB  - We study a new class of mean-field quadratic backward stochastic differential equations (qBSDEs) arising from mean-field portfolio games with exponential utility. Typical examples of such games include a mean-field portfolio game with price impact, and a finite-contract pricing model with market clearing conditions. Generators of these mean-field qBSDEs contain quadratic terms 𝔼[Z]^⊤ Z and |𝔼[Z]|^2, instead of the classical pathwise Z^⊤ Z term. We prove local well-posedness under L^q-integrability assumptions on terminals and their Malliavin derivatives, and global well-posedness under an extra exponential integrability condition on the Malliavin derivatives. Then we show the existence and uniqueness of global equilibria of the above two mean-field games via our qBSDE theory.
ER  -