Necessary and sufficient conditions for near-optimality of stochastic delay systems

作者：Wang, Yuan; Wu, Zhen^*

来源：International Journal of Control, 2018, 91(8): 1730-1744.

DOI：10.1080/00207179.2017.1327725

• Stochastic near-optimal control
• necessary and sufficient conditions
• stochastic differential delayed equations
• anticipated backward stochastic differential equations
• Ekeland's variational principle

In this paper, we study a class of near-optimisation problems with controlled systems described by the stochastic differential equations with delay. Thanks to the Ekeland's variational principle, we establish both necessary and sufficient conditions for the near-optimality of this problem by several delicate estimates for the state and adjoint processes. It is also shown that the error estimate for the near-optimality is of the order epsilon 1/2 exactly. Moreover, we consider a production and consumption choice problem with delay to illustrate the application of our theoretical results.

• 出版日期2018
• 单位山东大学