Abstract
This paper is concerned with a linear quadratic optimal control problem of delayed backward stochastic differential equations. An explicit representation is derived for the optimal control, which is a linear feedback of the entire past history and the future state trajectory in a short period of time. This is one of the major distinctive features of the delayed backward stochastic linear quadratic optimal control problem. To obtain the optimal feedback, a new class of delayed Riccati equations is introduced and the unique solvability of their solutions are discussed in detail.
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