Optimal control of linear backward stochastic differential equations with a quadratic cost criterion

摘要

Backward Stochastic Differential Equations (BSDEs) are Ito SDEs with a random terminal condition. While it is the case that nncontrolled BSDEs have been the topic of extensive research for a number of years, little has been done on optimal control of BSDEs. In this paper, we consider the problem of linear-quadratic control of a BSDE. A complete solution to this problem is obtained, in terms of a pair of Riccati type equations and an uncontrolled BSDE, using an approach that is based on the completion of squares technique.