Necessary and Sufficient Conditions of Optimalcontrol for Infinite Dimensional SDEs
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.
KeywordsMartingale Optimal control Backward stochastic differential equation Maximum principle Conditions of optimality
Mathematical Subject Classification 201060H10 60G44
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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