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Necessary and sufficient conditions for optimal control of coupled forward-backward stochastic control systems driven by G-Brownian motion

  • Xiaojuan Li
  • Mingshang Hu
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Abstract

In this paper, we study a coupled forward-backward stochastic control system driven by G-Brownian motion. Based on some detailed estimates for control system, we obtain the variational inequality for cost functional, which is a necessary condition for optimality. Furthermore, we prove that this necessary condition is also a sufficient condition under the usual convexity assumptions.

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Cite

BibTeXRIS
BibTeX
@misc{li2026necessary,
  title = {{Necessary and sufficient conditions for optimal control of coupled forward-backward stochastic control systems driven by G-Brownian motion}},
  author = {Xiaojuan Li and Mingshang Hu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.29494},
  eprint = {2610.29494},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.29494},
}
RIS
TY  - UNPB
TI  - Necessary and sufficient conditions for optimal control of coupled forward-backward stochastic control systems driven by G-Brownian motion
AU  - Xiaojuan Li
AU  - Mingshang Hu
PY  - 2026
DA  - 2026/10/21
PB  - arXiv
DO  - 10.48550/arxiv.2610.29494
UR  - https://arxiv.org/abs/2610.29494
AB  - In this paper, we study a coupled forward-backward stochastic control system driven by G-Brownian motion. Based on some detailed estimates for control system, we obtain the variational inequality for cost functional, which is a necessary condition for optimality. Furthermore, we prove that this necessary condition is also a sufficient condition under the usual convexity assumptions.
ER  -