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From economics point of view, we investigate a new optimal control problemdriven by a stochastic differential equation with a multi-time states costfunctional. By constructing a series of first-order adjoint equations, weestablish the stochastic maximum principle and sufficient optimality conditionsfor this new optimal control problem. A constraints problem also be studied. Inthe end, we develop a near optimal control problem for a general costfunctional.

The necessary and sufficient conditions for stochastic differential systems with multi-time states cost functional