Regularity of Backward Stochastic Volterra Integral Equations in Hilbert Spaces

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Stochastic Analysis and Applications, ISSN: 0736-2994, Vol: 29, Issue: 1, Page: 146-168

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Vo V. Anh; Wilfried Grecksch; Jiongmin Yong
Informa UK Limited
Mathematics; Decision Sciences; Pontryagin maximum principle; Regularity of adapted solutions; Stochastic optimal control; Stochastic Volterra integral equations; COHERENT; UTILITY; DRIVEN; RISK; Mathematics; Applied; Statistics & Probability
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This article investigates backward stochastic Volterra integral equations in Hilbert spaces. The existence and uniqueness of their adapted solutions is reviewed. We establish the regularity of the adapted solutions to such equations by means of Malliavin calculus. For an application, we study an optimal control problem for a stochastic Volterra integral equation driven by a Hilbert space-valued fractional Brownian motion. A Pontryagin-type maximum principle is formulated for the problem and an example is presented. © Taylor & Francis Group, LLC.