Extended MF-AFBSDDEswCN and stochastic optimal controls of linear system
Abstract
The research studies the extended mean-field anticipated forward-backward stochastic delayed differential equations with common noise (extended MF-AFBSDDEswCN) by expanding the domination-monotonicity conditions. We generalize the conditions from a linear setting to a nonlinear one by including nonlinear adjoint functions which are key to guaranteeing the well-posedness of extended MF-AFBSDDEswCN. Utilizing this broader well-posedness framework for extended MF-AFBSDDEswCN, combined with other refined analytical tools, we examine two classes of stochastic optimal control problems. These include a linear-convex problem and a linear-quadratic problem with input constraints that can be both time-dependent and random. Moreover, the control elements regarding the initial values are path-dependent, which will cause some essential difficulties. For each problem, we establish the existence and uniqueness of optimal controls and provide their explicit, closed-form representations.
Related
- Ergodic Linear-Quadratic Optimal Control with Stochastic Coefficients
- Addendum to "Optimal Steering of a Linear Stochastic System to a Final Probability Distribution, Part II"
- Turnpike Properties for Exploratory Stochastic Linear-Quadratic Optimal Control with Indefinite Cost Functionals
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BibTeX
@misc{wu2026extended,
title = {{Extended MF-AFBSDDEswCN and stochastic optimal controls of linear system}},
author = {Hao Wu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.19779},
eprint = {2609.19779},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.19779},
}
RIS
TY - UNPB
TI - Extended MF-AFBSDDEswCN and stochastic optimal controls of linear system
AU - Hao Wu
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.19779
UR - https://arxiv.org/abs/2609.19779
AB - The research studies the extended mean-field anticipated forward-backward stochastic delayed differential equations with common noise (extended MF-AFBSDDEswCN) by expanding the domination-monotonicity conditions. We generalize the conditions from a linear setting to a nonlinear one by including nonlinear adjoint functions which are key to guaranteeing the well-posedness of extended MF-AFBSDDEswCN. Utilizing this broader well-posedness framework for extended MF-AFBSDDEswCN, combined with other refined analytical tools, we examine two classes of stochastic optimal control problems. These include a linear-convex problem and a linear-quadratic problem with input constraints that can be both time-dependent and random. Moreover, the control elements regarding the initial values are path-dependent, which will cause some essential difficulties. For each problem, we establish the existence and uniqueness of optimal controls and provide their explicit, closed-form representations.
ER -