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Necessary and Sufficient Conditions of Optimalcontrol for Infinite Dimensional SDEs

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Statistical Methods and Applications in Insurance and Finance (CIMPA School 2013)

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Abstract

A general maximum principle (necessary and sufficient conditions) for an optimal control problem governed by a stochastic differential equation driven by an infinite dimensional martingale is established. The solution of this equation takes its values in a separable Hilbert space and the control domain need not be convex when studying optimality necessary conditions. The result is obtained by using the adjoint backward stochastic differential equation.

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Acknowledgments

The author would like to thank the Mathematics Institute, Warwick University, where part of this work was done, for hospitality during the summer of 2011. Many thanks and much gratitude to King Abdulaziz City for Science and Technology (KACST), Riyadh, Saudi Arabia, for their support.

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Authors and Affiliations

  1. Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah, 51452, Saudi Arabia

    Abdulrahman Al-Hussein

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  1. Abdulrahman Al-Hussein
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Correspondence to Abdulrahman Al-Hussein .

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Editors and Affiliations

  1. Department of Mathematics, Université Cadi Ayyad Department of Mathematics, Marrakesh, Morocco

    M'hamed Eddahbi

  2. Faculté Polydisciplinaire, Université Cadi Ayyad, Safi, Morocco

    El Hassan Essaky

  3. Faculty of Mathematics, University of Barcelona, Barcelona, Spain

    Josep Vives

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Al-Hussein, A. (2016). Necessary and Sufficient Conditions of Optimalcontrol for Infinite Dimensional SDEs. In: Eddahbi, M., Essaky, E., Vives, J. (eds) Statistical Methods and Applications in Insurance and Finance. CIMPA School 2013. Springer Proceedings in Mathematics & Statistics, vol 158. Springer, Cham. https://doi.org/10.1007/978-3-319-30417-5_6

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