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Journal Articles Afrika Matematika Year : 2017

On optimal control of forward backward stochastic differential equations

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Fouzia Baghery
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Nabil Khelfallah
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B. Mezerdi
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Isabelle Turpin

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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hal-03149997 , version 1 (04-07-2022)

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