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On optimal control of forward backward stochastic differential equations

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 cadlag functions, endowed with the Jakubowsky Stopology. Moreover, under some convexity assumptions, we show that the relaxed optimal control is realized by a strict control.
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https://hal-uphf.archives-ouvertes.fr/hal-03149997
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Submitted on : Monday, July 4, 2022 - 3:49:17 PM
Last modification on : Tuesday, August 2, 2022 - 3:12:45 AM

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Fouzia Baghery, Nabil Khelfallah, B. Mezerdi, Isabelle Turpin. On optimal control of forward backward stochastic differential equations. Afrika Matematika, Springer, 2017, 28 (7-8), pp.1075-1092. ⟨10.1007/s13370-017-0504-x⟩. ⟨hal-03149997⟩

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