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Necessary and Sufficient Conditions of Optimalcontrol for Infinite Dimensional SDEs

  • Abdulrahman Al-HusseinEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 158)

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.

Keywords

Martingale Optimal control Backward stochastic differential equation Maximum principle Conditions of optimality 

Mathematical Subject Classification 2010

60H10 60G44 

Notes

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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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of MathematicsCollege of Science, Qassim UniversityBuraydahSaudi Arabia

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