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arXiv · 1701.08392

On optimal control of forward backward stochastic differential equations

Fouzia Baghery·Nabil Khelfallah·Brahim Mezerdi·Isabelle Turpin
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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.

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Fouzia Baghery, Nabil Khelfallah, Brahim Mezerdi, Isabelle Turpin. 2017-01-29. On optimal control of forward backward stochastic differential equations. https://arxiv.org/abs/1701.08392

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