BDSVIEs are defined and proven well-posed via M-solutions; a comparison theorem yields existence results for continuous coefficients, a duality with FDSVIEs is shown, and a maximum principle is derived for optimal control problems.
Optimal control of forward-backward stochastic Volterra equations
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abstract
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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2019 1verdicts
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Backward doubly stochastic Volterra integral equations and applications to optimal control problems
BDSVIEs are defined and proven well-posed via M-solutions; a comparison theorem yields existence results for continuous coefficients, a duality with FDSVIEs is shown, and a maximum principle is derived for optimal control problems.