Non-Linear Partial Differential Equations, Mathematical Physics, and Stochastic Analysis

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pp: 3–35

DOI: 10.4171/186-1/1

Optimal control of forward-backward stochastic Volterra equations

Nacira Agram[1], Bernt Øksendal[2] and Samia Yakhlef[3]

(1) University of Oslo, Norway
(2) University of Oslo, Norway
(3) University of Biskra, Algeria

We study the problem of optimal control of a coupled system of forward-backward stochastic Volterra equations. We use Hida–Malliavin calculus to prove a sufficient and a necessary maximum principle for the optimal control of such systems. Existence and uniqueness of backward stochastic Volterra integral equations are proved. As an application of our methods, we solve a recursive utility optimisation problem in a financial model with memory.

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