Optimality Conditions in One Stochastic Control Problem

Abstract

For one stochastic optimal control problem described by a linear Ito stochastic equation and linear quality functional a necessary and sufficient optimality condition form of the Pontryagin maximum principle is obtained. In the case of convexity of the nonlinear quality functional, a sufficient optimality condition is obtained. In the deterministic case, many authors have studied such problems using the increment method. The considered work using a stochastic analogue of the increment method necessary and sufficient conditions for optimality as well as sufficient conditions are established.

Keywords

• Ito equations
• optimal control
• optimality conditions

References

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