Maximum principle for optimal control of fully coupled mean-field
forward-backward stochastic differential equations with Teugels
martingales under partial observation
- MUTHUKUMAR P,
- G. Saranya,
- Mokhtar HAFAYED
MUTHUKUMAR P
The Gandhigram Rural Institute Deemed University Department of Mathematics
Corresponding Author:pmuthukumargri@gmail.com
Author ProfileG. Saranya
The Gandhigram Rural Institute Deemed University Department of Mathematics
Author ProfileAbstract
The necessary conditions for the optimal control of partially observed,
fully coupled forward-backward mean-field stochastic differential
equations driven by Teugels martingales are discussed in this paper. In
this context, we make the assumption that the forward diffusion
coefficient and the martingale coefficient are independent of the
control variable, and the control domain may not necessarily be convex.
For this class of optimal control problems, we derive the stochastic
maximum principle based on the classical method of spike variations and
the filtering techniques. The adjoint processes that are related to the
variational equations are determined by the solutions of proposed
forward-backward stochastic differential equations in finite-dimensional
spaces. Further, the Hamiltonian function is used to obtain the maximum
principle for the optimality of the given control system. Our results
are then applied to the mean-field type problem of linear quadratic
stochastic optimization.27 Sep 2023Submitted to Optimal Control, Applications and Methods 27 Sep 2023Submission Checks Completed
27 Sep 2023Assigned to Editor
27 Sep 2023Review(s) Completed, Editorial Evaluation Pending
16 Oct 2023Reviewer(s) Assigned
09 Apr 2024Editorial Decision: Revise Minor
18 Aug 20241st Revision Received
20 Aug 2024Submission Checks Completed
20 Aug 2024Assigned to Editor
20 Aug 2024Review(s) Completed, Editorial Evaluation Pending
21 Sep 2024Reviewer(s) Assigned
20 Oct 2024Editorial Decision: Accept