On optimal control of forward backward stochastic differential equations
Optimization and Control
2017-01-31 v1 Probability
Abstract
We consider a control problem where the system is driven by a decoupled as well as a coupled forward-backward stochastic differential equation. We prove the existence of an optimal control in the class of relaxed controls, which are measure-valued processes, generalizing the usual strict controls. The proof is based on some tightness properties and weak convergence on the space D of c\`adl\`ag functions, endowed with the Jakubowsky S-topology. Moreover, under some convexity assumptions, we show that the relaxed optimal control is realized by a strict control.
Cite
@article{arxiv.1701.08392,
title = {On optimal control of forward backward stochastic differential equations},
author = {Fouzia Baghery and Nabil Khelfallah and Brahim Mezerdi and Isabelle Turpin},
journal= {arXiv preprint arXiv:1701.08392},
year = {2017}
}
Comments
15 pages, submitted for publication in Afrika Matematika