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