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A global stochastic maximum principle for forward-backward stochastic control systems with quadratic convex generator and unbounded terminal condition

  • Ying Hu
  • Feng Li
  • Jiaqiang Wen
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Abstract

In this paper, we study a stochastic optimal control problem for forward-backward stochastic control systems with quadratic convex generator and unbounded terminal condition, where the control domain is not necessarily convex. Since the existing bounded mean oscillation (BMO) martingale approach used in the setting of quadratic BSDEs with bounded terminal conditions is not directly applicable to the present setting, we introduce a new probability measure, under which all subsequent analysis is then carried out. Finally, a global stochastic maximum principle is obtained.

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Cite

BibTeXRIS
BibTeX
@misc{hu2026global,
  title = {{A global stochastic maximum principle for forward-backward stochastic control systems with quadratic convex generator and unbounded terminal condition}},
  author = {Ying Hu and Feng Li and Jiaqiang Wen},
  howpublished = {HAL},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21451},
  eprint = {2609.21451},
  archivePrefix = {arXiv},
  url = {https://hal.science/hal-05768829v1},
}
RIS
TY  - UNPB
TI  - A global stochastic maximum principle for forward-backward stochastic control systems with quadratic convex generator and unbounded terminal condition
AU  - Ying Hu
AU  - Feng Li
AU  - Jiaqiang Wen
PY  - 2026
DA  - 2026/09/28
PB  - HAL
DO  - 10.48550/arxiv.2609.21451
UR  - https://hal.science/hal-05768829v1
AB  - In this paper, we study a stochastic optimal control problem for forward-backward stochastic control systems with quadratic convex generator and unbounded terminal condition, where the control domain is not necessarily convex. Since the existing bounded mean oscillation (BMO) martingale approach used in the setting of quadratic BSDEs with bounded terminal conditions is not directly applicable to the present setting, we introduce a new probability measure, under which all subsequent analysis is then carried out. Finally, a global stochastic maximum principle is obtained.
ER  -